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Publications

Publications of our group

Note

This page is currently under construction and extremely incomplete, until the coupling to the PUMA bibliography system is realized. Please refer to the publication list of Prof. Dr. B. Haasdonk until then.

Publications

2021
1. P. Buchfink and B. Haasdonk, “Experimental Comparison of Symplectic and Non-symplectic Model Order Reduction an Uncertainty Quantification Problem,” in Numerical Mathematics and Advanced Applications ENUMATH 2019, 2021, vol. 139. doi: 10.1007/978-3-030-55874-1.
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  @inproceedings{buchfink2021experimental, author = {Buchfink, Patrick and Haasdonk, Bernard}, booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2019}, doi = {10.1007/978-3-030-55874-1}, editor = {Vermolen, Fred J. and Vuik, Cornelis}, isbn = {978-3-030-55873-4}, issn = {1439-7358}, publisher = {Springer International Publishing}, title = {Experimental Comparison of Symplectic and Non-symplectic Model Order Reduction an Uncertainty Quantification Problem}, url = {https://www.springer.com/gp/book/9783030558734}, volume = 139, year = 2021 }
  Link
  https://www.springer.com/gp/book/9783030558734
2. B. Haasdonk, T. Wenzel, G. Santin, and S. Schmitt, “Biomechanical Surrogate Modelling Using Stabilized Vectorial Greedy Kernel Methods,” in Numerical Mathematics and Advanced Applications ENUMATH 2019, Cham, 2021, pp. 499--508.
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  @inproceedings{haasdonk2021biomechanical, address = {Cham}, author = {Haasdonk, Bernard and Wenzel, Tizian and Santin, Gabriele and Schmitt, Syn}, booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2019}, editor = {Vermolen, Fred J. and Vuik, Cornelis}, isbn = {978-3-030-55874-1}, pages = {499--508}, publisher = {Springer International Publishing}, title = {Biomechanical Surrogate Modelling Using Stabilized Vectorial Greedy Kernel Methods}, year = 2021 }
2020
1. P. Buchfink, B. Haasdonk, and S. Rave, “PSD-Greedy Basis Generation for Structure-Preserving Model Order Reduction of Hamiltonian Systems,” in Proceedings of the Conference Algoritmy 2020, Aug. 2020, pp. 151--160. [Online]. Available: http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1577/829
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  @inproceedings{Buchfink2020a, abstract = {Hamiltonian systems are central in the formulation of non-dissipative physical systems. They are characterized by a phase-space, a symplectic form and a Hamiltonian function. In numerical simulations of Hamiltonian systems, algorithms show improved accuracy when the symplectic structure is preserved [10]. For structure-preserving model order reduction (MOR) of Hamiltonian systems, symplectic MOR [17, 14, 11, 3, 16] can be used. It is based on a reduced-order basis that is symplectic, which requires symplectic basis generation techniques. In our work, we discuss greedy algorithms for symplectic basis generation. We complement the procedure presented in [14] with ideas of the POD-greedy [9], which results in a new greedy symplectic basis generation technique, the PSD-greedy. Inspired by POD-greedy, we use compression techniques in the greedy iterations to enrich the basis iteratively. We prove that this algorithm computes a symplectic basis when symplectic techniques are used for compression. In the numerical experiments, we compare the discussed methods for a linear elasticity problem. The results show that improvements of up to one order of magnitude in the relative reduction error are achievable with the new basis generation technique compared to the existing greedy approach from [14].}, author = {Buchfink, P. and Haasdonk, B. and Rave, S.}, booktitle = {Proceedings of the Conference Algoritmy 2020}, editor = {Frolkovič, P. and Mikula, K. and Ševčovič, D.}, isbn = {978-80-227-5032-5}, month = {08}, pages = {151--160}, publisher = {Vydavateľstvo SPEKTRUM}, title = {PSD-Greedy Basis Generation for Structure-Preserving Model Order Reduction of Hamiltonian Systems}, url = {http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1577/829}, year = 2020 }
  Link
  http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1577/829
2019
1. T. Brünnette, G. Santin, and B. Haasdonk, “Greedy Kernel Methods for Accelerating Implicit Integrators for Parametric ODEs,” in Numerical Mathematics and Advanced Applications - ENUMATH 2017, Cham, 2019, pp. 889--896.
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  @inproceedings{Bruennette2019, abstract = {We present a novel acceleration method for the solution of parametric ODEs by single-step implicit solvers by means of greedy kernel-based surrogate models. In an offline phase, a set of trajectories is precomputed with a high-accuracy ODE solver for a selected set of parameter samples, and used to train a kernel model which predicts the next point in the trajectory as a function of the last one. This model is cheap to evaluate, and it is used in an online phase for new parameter samples to provide a good initialization point for the nonlinear solver of the implicit integrator. The accuracy of the surrogate reflects into a reduction of the number of iterations until convergence of the solver, thus providing an overall speedup of the full simulation. Interestingly, in addition to providing an acceleration, the accuracy of the solution is maintained, since the ODE solver is still used to guarantee the required precision. Although the method can be applied to a large variety of solvers and different ODEs, we will present in details its use with the Implicit Euler method for the solution of the Burgers equation, which results to be a meaningful test case to demonstrate the method's features.}, address = {Cham}, author = {Br{\"u}nnette, Tim and Santin, Gabriele and Haasdonk, Bernard}, booktitle = {Numerical Mathematics and Advanced Applications - ENUMATH 2017}, editor = {Radu, Florin Adrian and Kumar, Kundan and Berre, Inga and Nordbotten, Jan Martin and Pop, Iuliu Sorin}, isbn = {978-3-319-96415-7}, owner = {santinge}, pages = {889--896}, publisher = {Springer International Publishing}, title = {Greedy Kernel Methods for Accelerating Implicit Integrators for Parametric {ODE}s}, year = 2019 }
2. P. Buchfink, A. Bhatt, and B. Haasdonk, “Symplectic Model Order Reduction with Non-Orthonormal Bases,” Mathematical and Computational Applications, vol. 24, no. 2, Art. no. 2, 2019, doi: 10.3390/mca24020043.
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  @article{buchfink2019symplectic, affiliation = {Buchfink, P (Reprint Author), Univ Stuttgart, Inst Appl Anal & Numer Simulat, D-70569 Stuttgart, Germany. Buchfink, Patrick; Haasdonk, Bernard, Univ Stuttgart, Inst Appl Anal & Numer Simulat, D-70569 Stuttgart, Germany. Bhatt, Ashish, Indian Inst Technol ISM, Dhanbad 826004, Jharkhand, India.}, author = {Buchfink, Patrick and Bhatt, Ashish and Haasdonk, Bernard}, doi = {10.3390/mca24020043}, issn = {{1300-686X} and {2297-8747}}, journal = {Mathematical and Computational Applications}, language = {eng}, number = 2, pages = 43, publisher = {MDPI}, research-areas = {Mathematics}, title = {Symplectic Model Order Reduction with Non-Orthonormal Bases}, unique-id = {ISI:000483307400010}, volume = 24, year = 2019 }
3. K. Carlberg, L. Brencher, B. Haasdonk, and A. Barth, “Data-Driven Time Parallelism via Forecasting,” SIAM Journal on Scientific Computing, vol. 41, no. 3, Art. no. 3, 2019, doi: 10.1137/18M1174362.
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  @article{CBHB19, author = {Carlberg, K. and Brencher, L. and Haasdonk, Bernard and Barth, A.}, doi = {10.1137/18M1174362}, eprint = {https://doi.org/10.1137/18M1174362}, file = {:PDF/CBHB16_www_arxiv_forecasting_time_parallelization.pdf:PDF}, groups = {haasdonk_misc, haasdonk_all_papers}, journal = {SIAM Journal on Scientific Computing}, number = 3, owner = {santinge}, pages = {B466-B496}, title = {Data-Driven Time Parallelism via Forecasting}, url = {https://arxiv.org/abs/1610.09049v1}, volume = 41, year = 2019 }
  Link
  https://arxiv.org/abs/1610.09049v1
4. A. Denzel, B. Haasdonk, and J. Kästner, “Gaussian Process Regression for Minimum Energy Path Optimization and Transition State Search,” J. Phys. Chem. A, vol. 123, no. 44, Art. no. 44, 2019, [Online]. Available: https://doi.org/10.1021/acs.jpca.9b08239
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  @article{dhk2019, author = {Denzel, A. and Haasdonk, Bernard and K\"astner, J.}, journal = {J. Phys. Chem. A}, number = 44, pages = {9600--9611}, title = {Gaussian Process Regression for Minimum Energy Path Optimization and Transition State Search}, url = {https://doi.org/10.1021/acs.jpca.9b08239}, volume = 123, year = 2019 }
  Link
  https://doi.org/10.1021/acs.jpca.9b08239
5. M. Köppel et al., “Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario,” Comput. Geosci., vol. 2, no. 23, Art. no. 23, 2019, doi: https://doi.org/10.1007/s10596-018-9785-x.
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  @article{koppel2017comparison, abstract = {A variety of methods is available to quantify uncertainties arising within the modeling of flow and transport in carbon dioxide storage, but there is a lack of thorough comparisons. Usually, raw data from such storage sites can hardly be described by theoretical statistical distributions since only very limited data is available. Hence, exact information on distribution shapes for all uncertain parameters is very rare in realistic applications. We discuss and compare four different methods tested for data-driven uncertainty quantification based on a benchmark scenario of carbon dioxide storage. In the benchmark, for which we provide data and code, carbon dioxide is injected into a saline aquifer modeled by the nonlinear capillarity-free fractional flow formulation for two incompressible fluid phases, namely carbon dioxide and brine. To cover different aspects of uncertainty quantification, we incorporate various sources of uncertainty such as uncertainty of boundary conditions, of conceptual model definitions and of material properties. We consider recent versions of the following non-intrusive and intrusive uncertainty quantification methods: arbitary polynomial chaos, spatially adaptive sparse grids, kernel-based greedy interpolation and hybrid stochastic Galerkin. The performance of each approach is demonstrated assessing expectation value and standard deviation of the carbon dioxide saturation against a reference statistic based on Monte Carlo sampling. We compare the convergence of all methods reporting on accuracy with respect to the number of model runs and resolution. Finally we offer suggestions about the methods� advantages and disadvantages that can guide the modeler for uncertainty quantification in carbon dioxide storage and beyond.}, author = {K\{"o}ppel, M. and Franzelin, F. and Kr\{"o}ker, I. and Oladyshkin, S. and Santin, G. and Wittwar, D. and Barth, A. and Haasdonk, B. and Nowak, W. and Pfl\{"u}ger, D. and Rohde, C.}, doi = {https://doi.org/10.1007/s10596-018-9785-x}, journal = {Comput. Geosci.}, number = 23, owner = {santinge}, pages = {339-354}, publisher = {Springer International Publishing}, title = {Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario}, url = {https://doi.org/10.1007/s10596-018-9785-x}, volume = 2, year = 2019 }
  Link
  https://doi.org/10.1007/s10596-018-9785-x
6. G. Santin and B. Haasdonk, “Kernel Methods for Surrogate Modelling,” University of Stuttgart, 2019.
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  @techreport{SantinHaasdonkKernelChapter2019, author = {Santin, G. and Haasdonk, Bernard}, institution = {University of Stuttgart}, note = {https://www.ians.uni-stuttgart.de/anm/publications/files\_publication\_anm/SH2019.pdf}, title = {Kernel Methods for Surrogate Modelling}, year = 2019 }
7. G. Santin, D. Wittwar, and B. Haasdonk, “Sparse approximation of regularized kernel interpolation by greedy algorithms,” 2019.
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  @techreport{Santin2019a, author = {Santin, Gabriele and Wittwar, Dominik and Haasdonk, Bernard}, title = {Sparse approximation of regularized kernel interpolation by greedy algorithms}, year = 2019 }
8. G. Santin and B. Haasdonk, “Kernel Methods for Surrogate Modeling,” ArXiv 1907.10556, 2019. [Online]. Available: https://arxiv.org/abs/1907.10556
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  @techreport{SaHa2019a, author = {Santin, Gabriele and Haasdonk, Bernard}, file = {:PDF/SaHa2019a_kernel_chapter.pdf:PDF}, number = {1907.10556}, owner = {santinge}, title = {Kernel Methods for Surrogate Modeling}, type = {ArXiv}, url = {https://arxiv.org/abs/1907.10556}, year = 2019 }
  Link
  https://arxiv.org/abs/1907.10556
9. A. Schmidt, D. Wittwar, and B. Haasdonk, “Rigorous and effective a-posteriori error bounds for nonlinear problems -- Application to RB methods,” Advances in Computational Mathematics, 2019, doi: 10.1007/s10444-019-09730-9.
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  @article{SWH2019, author = {Schmidt, A. and Wittwar, D. and Haasdonk, Bernard}, doi = {10.1007/s10444-019-09730-9}, journal = {Advances in Computational Mathematics}, title = {Rigorous and effective a-posteriori error bounds for nonlinear problems -- {A}pplication to {RB} methods}, year = 2019 }
10. T. Wenzel, G. Santin, and B. Haasdonk, “A novel class of stabilized greedy kernel approximation algorithms: Convergence, stability & uniform point distribution.” 2019.
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  @misc{wenzel2019novel, archiveprefix = {arXiv}, author = {Wenzel, Tizian and Santin, Gabriele and Haasdonk, Bernard}, eprint = {1911.04352}, primaryclass = {math.NA}, title = {A novel class of stabilized greedy kernel approximation algorithms: Convergence, stability \& uniform point distribution}, year = 2019 }
11. D. Wittwar, G. Santin, and B. Haasdonk, “Part II on matrix valued kernels including analysis,” 2019.
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  @techreport{Wittwar2019a, author = {Wittwar, Dominik and Santin, Gabriele and Haasdonk, Bernard}, title = {Part {II} on matrix valued kernels including analysis}, year = 2019 }
12. D. Wittwar and B. Haasdonk, “Greedy Algorithms for Matrix-Valued Kernels,” in Numerical Mathematics and Advanced Applications ENUMATH 2017, Cham, 2019, pp. 113--121.
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  @inproceedings{WH18a, abstract = {a.}, address = {Cham}, author = {Wittwar, Dominik and Haasdonk, Bernard}, booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2017}, editor = {Radu, Florin Adrian and Kumar, Kundan and Berre, Inga and Nordbotten, Jan Martin and Pop, Iuliu Sorin}, isbn = {978-3-319-96415-7}, pages = {113--121}, publisher = {Springer International Publishing}, title = {Greedy Algorithms for Matrix-Valued Kernels}, year = 2019 }
2018
1. B. M. Afkham, A. Bhatt, B. Haasdonk, and J. S. Hesthaven, “Symplectic Model-Reduction with a Weighted Inner Product,” 2018.
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  @unpublished{afkham2018symplectic, author = {Afkham, Babak Maboudi and Bhatt, Ashish and Haasdonk, Bernard and Hesthaven, Jan S.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Afkham2018_www.pdf:PDF}, note = {Submitted}, owner = {bhattah}, title = {Symplectic Model-Reduction with a Weighted Inner Product}, year = 2018 }
2. A. Bhatt and B. Haasdonk, “Certified and structure-preserving model order reduction of EMBS,” RAMSA 2017, New Delhi. 2018.
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  @misc{AshishBhatt2018, author = {Bhatt, Ashish and Haasdonk, Bernard}, istalk = {yes}, journal = {RAMSA 2017, New Delhi}, owner = {bhattah}, title = {Certified and structure-preserving model order reduction of EMBS}, year = 2018 }
3. A. Bhatt, B. Haasdonk, and B. E. Moore, “Structure-preserving Integration and Model Order Reduction,” Invited online talk in Department of Mathematics, IIT Roorkee. 2018.
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  @misc{AshishBhatt2018a, author = {Bhatt, Ashish and Haasdonk, Bernard and Moore, Brian E}, istalk = {yes}, journal = {Invited online talk in Department of Mathematics, IIT Roorkee}, owner = {bhattah}, title = {Structure-preserving Integration and Model Order Reduction}, year = 2018 }
4. T. Brünnette, G. Santin, and B. Haasdonk, “Greedy kernel methods for accelerating implicit integrators for parametric ODEs,” 2018.
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  @inproceedings{BSH18, author = {Br{\"u}nnette, T. and Santin, G. and Haasdonk, Bernard}, booktitle = {Proc. ENUMATH 2017}, note = {Submitted}, owner = {haasdonk}, title = {Greedy kernel methods for accelerating implicit integrators for parametric ODEs}, year = 2018 }
5. C. Dibak, B. Haasdonk, A. Schmidt, F. Dürr, and K. Rothermel, “Enabling interactive mobile simulations through distributed reduced models,” Pervasive and Mobile Computing, Elsevier BV, vol. 45, pp. 19--34, 2018, doi: https://doi.org/10.1016/j.pmcj.2018.02.002.
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  @article{Dibak2018, abstract = {Abstract Currently, various hardware and software companies are developing augmented reality devices, most prominently Microsoft with its Hololens. Besides gaming, such devices can be used for serious pervasive applications, like interactive mobile simulations to support engineers in the field. Interactive simulations have high demands on resources, which the mobile device alone is unable to satisfy. Therefore, we propose a framework to support mobile simulations by distributing the computation between the mobile device and a remote server based on the reduced basis method. Evaluations show that we can speed-up the numerical computation by over 131 times while using 73 times less energy.}, author = {Dibak, Christoph and Haasdonk, Bernard and Schmidt, Andreas and D{\"u}rr, Frank and Rothermel, Kurt}, doi = {https://doi.org/10.1016/j.pmcj.2018.02.002}, issn = {1574-1192}, journal = {Pervasive and Mobile Computing, Elsevier BV}, pages = {19--34}, title = {Enabling interactive mobile simulations through distributed reduced models}, url = {https://www.sciencedirect.com/science/article/pii/S1574119217304704}, volume = 45, year = 2018 }
  Link
  https://www.sciencedirect.com/science/article/pii/S1574119217304704
6. J. Fehr, D. Grunert, A. Bhatt, and B. Haasdonk, “A Sensitivity Study of Error Estimation in Reduced Elastic Multibody Systems,” 2018.
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  @inproceedings{Fehr2018, author = {Fehr, J. and Grunert, D. and Bhatt, A. and Haasdonk, Bernard}, booktitle = {Proceedings of MATHMOD 2018, Vienna, Austria}, file = {:PDF/Fehr2017_www.pdf:PDF}, groups = {bhatt}, owner = {bhattah}, title = {A Sensitivity Study of Error Estimation in Reduced Elastic Multibody Systems}, year = 2018 }
7. F. Fritzen, B. Haasdonk, D. Ryckelynck, and S. Schöps, “An algorithmic comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a nonlinear thermal problem,” Math. Comput. Appl. 2018, vol. 23, no. 1, Art. no. 1, 2018, doi: doi:10.3390/mca23010008.
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  @article{fritzen2018algorithmic, author = {Fritzen, Felix and Haasdonk, Bernard and Ryckelynck, David and Schöps, Sebastian}, doi = {doi:10.3390/mca23010008}, institution = {University of Stuttgart}, journal = {Math. Comput. Appl. 2018}, number = 1, owner = {haasdonk}, title = {An algorithmic comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a nonlinear thermal problem}, type = {Arxiv Report}, url = {http://www.mdpi.com/2297-8747/23/1/8/pdf}, volume = 23, year = 2018 }
  Link
  http://www.mdpi.com/2297-8747/23/1/8/pdf
8. B. Haasdonk, B. Hamzi, G. Santin, and D. Wittwar, “Greedy Kernel Methods for Center Manifold Approximation,” ArXiv 1810.11329, 2018.
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  @techreport{Boumediene2018, author = {Haasdonk, Bernard and Hamzi, Boumediene and Santin, Gabriele and Wittwar, Dominik}, number = {1810.11329}, owner = {santinge}, title = {Greedy Kernel Methods for Center Manifold Approximation}, type = {ArXiv}, year = 2018 }
9. B. Haasdonk and G. Santin, “Greedy Kernel Approximation for Sparse Surrogate Modeling,” in Reduced-Order Modeling (ROM) for Simulation and Optimization: Powerful Algorithms as Key Enablers for Scientific Computing, W. Keiper, A. Milde, and S. Volkwein, Eds. Cham: Springer International Publishing, 2018, pp. 21--45. doi: 10.1007/978-3-319-75319-5_2.
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  @incollection{SH2017b, abstract = {Modern simulation scenarios frequently require multi-query or real-time responses of simulation models for statistical analysis, optimization, or process control. However, the underlying simulation models may be very time-consuming rendering the simulation task difficult or infeasible. This motivates the need for rapidly computable surrogate models. We address the case of surrogate modeling of functions from vectorial input to vectorial output spaces. These appear, for instance, in simulation of coupled models or in the case of approximating general input--output maps. We review some recent methods and theoretical results in the field of greedy kernel approximation schemes. In particular, we recall the vectorial kernel orthogonal greedy algorithm (VKOGA) for approximating vector-valued functions. We collect some recent convergence statements that provide sound foundation for these algorithms, in particular quasi-optimal convergence rates in case of kernels inducing Sobolev spaces. We provide some initial experiments that can be obtained with non-symmetric greedy kernel approximation schemes. The results indicate better stability and overall more accurate models in situations where the input data locations are not equally distributed.}, address = {Cham}, author = {Haasdonk, Bernard and Santin, Gabriele}, booktitle = {Reduced-Order Modeling (ROM) for Simulation and Optimization: Powerful Algorithms as Key Enablers for Scientific Computing}, doi = {10.1007/978-3-319-75319-5_2}, editor = {Keiper, Winfried and Milde, Anja and Volkwein, Stefan}, isbn = {978-3-319-75319-5}, owner = {santinge}, pages = {21--45}, publisher = {Springer International Publishing}, title = {Greedy Kernel Approximation for Sparse Surrogate Modeling}, url = {https://doi.org/10.1007/978-3-319-75319-5_2}, year = 2018 }
  Link
  https://doi.org/10.1007/978-3-319-75319-5_2
10. T. Köppl, G. Santin, B. Haasdonk, and R. Helmig, “Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods,” International Journal for Numerical Methods in Biomedical Engineering, vol. 34, no. 8, Art. no. 8, 2018, doi: 10.1002/cnm.3095.
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  @article{KSHH2018, abstract = {Summary In this work, we consider two kinds of model reduction techniques to simulate blood flow through the largest systemic arteries, where a stenosis is located in a peripheral artery i.e. in an artery that is located far away from the heart. For our simulations we place the stenosis in one of the tibial arteries belonging to the right lower leg (right post tibial artery). The model reduction techniques that are used are on the one hand dimensionally reduced models (1â€D and 0â€D models, the soâ€called mixedâ€dimension model) and on the other hand surrogate models produced by kernel methods. Both methods are combined in such a way that the mixedâ€dimension models yield training data for the surrogate model, where the surrogate model is parametrised by the degree of narrowing of the peripheral stenosis. By means of a wellâ€trained surrogate model, we show that simulation data can be reproduced with a satisfactory accuracy and that parameter optimisation or state estimation problems can be solved in a very efficient way. Furthermore it is demonstrated that a surrogate model enables us to present after a very short simulation time the impact of a varying degree of stenosis on blood flow, obtaining a speedup of several orders over the full model.}, author = {K{\"o}ppl, Tobias and Santin, Gabriele and Haasdonk, Bernard and Helmig, Rainer}, doi = {10.1002/cnm.3095}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/cnm.3095}, file = {:PDF/KSHH2017_www_preprint.pdf:PDF}, groups = {haasdonk, santin}, journal = {International Journal for Numerical Methods in Biomedical Engineering}, note = {e3095 cnm.3095}, number = 8, owner = {santinge}, pages = {e3095}, title = {Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cnm.3095}, volume = 34, year = 2018 }
  Link
  https://onlinelibrary.wiley.com/doi/abs/10.1002/cnm.3095
11. G. Santin, D. Wittwar, and B. Haasdonk, “Greedy regularized kernel interpolation,” University of Stuttgart, ArXiv preprint 1807.09575, 2018.
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  @techreport{SaWiHa2018, author = {Santin, Gabriele and Wittwar, Dominik and Haasdonk, Bernard}, groups = {haasdonk, wittwar, santin}, institution = {University of Stuttgart}, number = {1807.09575}, owner = {santinge}, title = {Greedy regularized kernel interpolation}, type = {ArXiv preprint}, year = 2018 }
12. A. Schmidt and B. Haasdonk, “Data-driven surrogates of value functions and applications to feedback control for dynamical systems,” 2018. [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1766
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  @inproceedings{SH18f, author = {Schmidt, A. and Haasdonk, Bernard}, boottitle = {In Proc. of MATHMOD 2018}, groups = {haasdonk, schmidta, haasdonk_all_papers}, owner = {schmidta}, title = {Data-driven surrogates of value functions and applications to feedback control for dynamical systems}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1766}, year = 2018 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1766
13. A. Schmidt, D. Wittwar, and B. Haasdonk, “Rigorous and effective a-posteriori error bounds for nonlinear problems -- Application to RB methods,” University of Stuttgart, SimTech Preprint, 2018.
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  @techreport{SWH2018, __markedentry = {[haasdonk:6]}, author = {Schmidt, A. and Wittwar, D. and Haasdonk, Bernard}, institution = {University of Stuttgart}, owner = {haasdonk}, title = {Rigorous and effective a-posteriori error bounds for nonlinear problems -- {A}pplication to {RB} methods}, type = {SimTech Preprint}, year = 2018 }
14. A. Schmidt and B. Haasdonk, “Reduced basis approximation of large scale parametric algebraic Riccati equations,” ESAIM: Control, Optimisation and Calculus of Variations, vol. 24, no. 1, Art. no. 1, Jan. 2018, doi: 10.1051/cocv/2017011.
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  @article{SH18, author = {Schmidt, Andreas and Haasdonk, Bernard}, doi = {10.1051/cocv/2017011}, file = {:PDF/SH17_journal.pdf:PDF}, groups = {haasdonk, schmidta, haasdonk_all_papers}, issn = {1262-3377}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, month = {01}, number = 1, owner = {schmidta}, pages = {129--151}, publisher = {EDP Sciences}, title = {Reduced basis approximation of large scale parametric algebraic {Riccati} equations}, url = {http://dx.doi.org/10.1051/cocv/2017011}, volume = 24, year = 2018 }
  Link
  http://dx.doi.org/10.1051/cocv/2017011
15. D. Wittwar, G. Santin, and B. Haasdonk, “Interpolation with uncoupled separable matrix-valued kernels,” ArXiv e-prints, Jul. 2018.
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  BibTeX
  @article{2018arXiv180709111W, adsnote = {Provided by the SAO/NASA Astrophysics Data System}, adsurl = {http://adsabs.harvard.edu/abs/2018arXiv180709111W}, archiveprefix = {arXiv}, author = {Wittwar, D. and Santin, G. and Haasdonk, B.}, eprint = {1807.09111}, journal = {ArXiv e-prints}, month = {07}, primaryclass = {math.NA}, title = {Interpolation with uncoupled separable matrix-valued kernels}, year = 2018 }
16. D. Wittwar and B. Haasdonk, “Greedy Algorithms for Matrix-Valued Kernels,” University of Stuttgart, 2018. [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1773
  - BibTeX
  - Link
  BibTeX
  @techreport{wittwar2018greedy, abstract = {We are interested in approximating vector-valued functions on a compact set $\Omega\subset \mathbb R^d$. We consider reproducing kernel Hilbert spaces of $\mathbb R^m$-valued functions which each admit a unique matrix-valued reproducing kernel $k$. These spaces seem promising, when modelling correlations between the target function components. The approximation of a function is a linear combination of matrix-valued kernel evaluations multiplied with coefficient vectors. To guarantee a fast evaluation of the approximant the expansion size, i.e. the number of centers $n$ is desired to be small. We thus present three different greedy algorithms by which a suitable set of centers is chosen in an incremental fashion: First, the $P$-Greedy which requires no function evaluations, second and third, the $f$-Greedy and $f/P$-Greedy which require function evaluations but produce centers tailored to the target function. The efficiency of the approaches is investigated on some data from an artificial model.}, author = {Wittwar, Dominik and Haasdonk, Bernard}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/WH18_www_greedy_matrix_valued.pdf:PDF}, institution = {University of Stuttgart}, owner = {santinge}, title = {Greedy Algorithms for Matrix-Valued Kernels}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1773}, year = 2018 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1773
2017
1. A. Alla, B. Haasdonk, and A. Schmidt, “Feedback control of parametrized PDEs via model order reduction and dynamic programming principle,” University of Stuttgart, 2017. [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1765
  - BibTeX
  - Link
  BibTeX
  @techreport{AHS17, author = {Alla, A. and Haasdonk, Bernard and Schmidt, A.}, groups = {haasdonk, schmidta}, institution = {University of Stuttgart}, note = {Submitted}, owner = {schmidta}, title = {Feedback control of parametrized PDEs via model order reduction and dynamic programming principle}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1765}, year = 2017 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1765
2. A. Alla, M. Gunzburger, B. Haasdonk, and A. Schmidt, “Model order reduction for the control of parametrized partial differential equations via dynamic programming principle,” University of Stuttgart, 2017.
  - BibTeX
  BibTeX
  @techreport{AGHS2017, author = {Alla, A. and Gunzburger, M. and Haasdonk, Bernard and Schmidt, A.}, institution = {University of Stuttgart}, owner = {schmidta}, title = {Model order reduction for the control of parametrized partial differential equations via dynamic programming principle}, year = 2017 }
3. A. Alla, A. Schmidt, and B. Haasdonk, “Model Order Reduction Approaches for Infinite Horizon Optimal Control Problems via the HJB Equation,” in Model Reduction of Parametrized Systems, P. Benner, M. Ohlberger, A. Patera, G. Rozza, and K. Urban, Eds. Cham: Springer International Publishing, 2017, pp. 333--347. doi: 10.1007/978-3-319-58786-8_21.
  - BibTeX
  - Link
  BibTeX
  @inbook{alla2017model, abstract = {We investigate feedback control for infinite horizon optimal control problems for partial differential equations. The method is based on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is well-known that HJB equations suffer the so called curse of dimensionality and, therefore, a reduction of the dimension of the system is mandatory. In this report we focus on the infinite horizon optimal control problem with quadratic cost functionals. We compare several model reduction methods such as Proper Orthogonal Decomposition, Balanced Truncation and a new algebraic Riccati equation based approach. Finally, we present numerical examples and discuss several features of the different methods analyzing advantages and disadvantages of the reduction methods.}, address = {Cham}, author = {Alla, Alessandro and Schmidt, Andreas and Haasdonk, Bernard}, booktitle = {Model Reduction of Parametrized Systems}, doi = {10.1007/978-3-319-58786-8_21}, editor = {Benner, Peter and Ohlberger, Mario and Patera, Anthony and Rozza, Gianluigi and Urban, Karsten}, isbn = {978-3-319-58786-8}, owner = {schmidta}, pages = {333--347}, publisher = {Springer International Publishing}, title = {Model Order Reduction Approaches for Infinite Horizon Optimal Control Problems via the HJB Equation}, url = {https://doi.org/10.1007/978-3-319-58786-8_21}, year = 2017 }
  Link
  https://doi.org/10.1007/978-3-319-58786-8_21
4. U. Baur, P. Benner, B. Haasdonk, C. Himpe, I. Maier, and M. Ohlberger, “Comparison of methods for parametric model order reduction of instationary problems,” in Model Reduction and Approximation: Theory and Algorithms, P. Benner, A. Cohen, M. Ohlberger, and K. Willcox, Eds. SIAM Philadelphia, 2017. [Online]. Available: https://www2.mpi-magdeburg.mpg.de/preprints/2015/MPIMD15-01.pdf
  - BibTeX
  - Link
  BibTeX
  @incollection{BBHHMO2017, author = {Baur, U. and Benner, P. and Haasdonk, Bernard and Himpe, C. and Maier, I. and Ohlberger, M.}, booktitle = {Model Reduction and Approximation: Theory and Algorithms}, editor = {Benner, P. and Cohen, A. and Ohlberger, M. and Willcox, K.}, groups = {haasdonk, maieril, haasdonk_all_papers}, owner = {haasdonk}, publisher = {SIAM Philadelphia}, title = {Comparison of methods for parametric model order reduction of instationary problems}, url = {https://www2.mpi-magdeburg.mpg.de/preprints/2015/MPIMD15-01.pdf}, year = 2017 }
  Link
  https://www2.mpi-magdeburg.mpg.de/preprints/2015/MPIMD15-01.pdf
5. T. Brünnette, G. Santin, and B. Haasdonk, “Greedy kernel methods for accelerating implicit integrators for parametric ODEs,” University of Stuttgart, 2017. [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1767
  - BibTeX
  - Link
  BibTeX
  @techreport{Bruennette_Enumath2017, abstract = {We present a novel acceleration method for the solution of parametric ODEs by single-step implicit solvers by means of greedy kernel-based surrogate models. In an offline phase, a set of trajectories is precomputed with a high-accuracy ODE solver for a selected set of parameter samples, and used to train a kernel model which predicts the next point in the trajectory as a function of the last one. This model is cheap to evaluate, and it is used in an online phase for new parameter samples to provide a good initialization point for the nonlinear solver of the implicit integrator. The accuracy of the surrogate reflects into a reduction of the number of iterations until convergence of the solver, thus providing an overall speedup of the full simulation. Interestingly, in addition to providing an acceleration, the accuracy of the solution is maintained, since the ODE solver is still used to guarantee the required precision. Although the method can be applied to a large variety of solvers and different ODEs, we will present in details its use with the Implicit Euler method for the solution of the Burgers equation, which results to be a meaningful test case to demonstrate the method's features.}, author = {Br{\"u}nnette, Tim and Santin, Gabriele and Haasdonk, Bernard}, groups = {santin}, institution = {University of Stuttgart}, owner = {santinge}, title = {Greedy kernel methods for accelerating implicit integrators for parametric ODEs}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1767}, year = 2017 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1767
6. C. Dibak, A. Schmidt, F. Dürr, B. Haasdonk, and K. Rothermel, “Server-assisted interactive mobile simulations for pervasive applications,” in 2017 IEEE International Conference on Pervasive Computing and Communications (PerCom), Mar. 2017, pp. 111--120. doi: 10.1109/PERCOM.2017.7917857.
  - BibTeX
  BibTeX
  @inproceedings{Dibak2017, author = {Dibak, C. and Schmidt, A. and D{\"u}rr, F. and Haasdonk, Bernard and Rothermel, K.}, booktitle = {2017 IEEE International Conference on Pervasive Computing and Communications (PerCom)}, doi = {10.1109/PERCOM.2017.7917857}, groups = {haasdonk, schmidta}, month = {03}, owner = {schmidta}, pages = {111--120}, title = {Server-assisted interactive mobile simulations for pervasive applications}, year = 2017 }
7. B. Haasdonk, “Reduced Basis Methods for Parametrized PDEs -- A Tutorial Introduction for Stationary and Instationary Problems,” in Model Reduction and Approximation: Theory and Algorithms, P. Benner, A. Cohen, M. Ohlberger, and K. Willcox, Eds. SIAM, Philadelphia, 2017, pp. 65--136. [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=938
  - BibTeX
  - Link
  BibTeX
  @incollection{Haasdonk2017, author = {Haasdonk, Bernard}, booktitle = {Model Reduction and Approximation: Theory and Algorithms}, editor = {Benner, P. and Cohen, A. and Ohlberger, M. and Willcox, K.}, file = {:PDF/Haasdonk2014a_www_preprint_RBtutorial_with_update2016.pdf:PDF}, groups = {anm, haasdonk}, owner = {haasdonk}, pages = {65--136}, publisher = {SIAM, Philadelphia}, title = {Reduced Basis Methods for Parametrized {PDE}s -- A Tutorial Introduction for Stationary and Instationary Problems}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=938}, year = 2017 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=938
8. M. Köppel et al., “Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario,” University of Stuttgart, 2017. [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1759
  - BibTeX
  - Link
  BibTeX
  @techreport{koeppel2017, abstract = {A variety of methods is available to quantify uncertainties arising within the modeling of flow and transport in carbon dioxide storage, but there is a lack of thorough comparisons. Usually, raw data from such storage sites can hardly be described by theoretical statistical distributions since only very limited data is available. Hence, exact information on distribution shapes for all uncertain parameters is very rare in realistic applications. We discuss and compare four different methods tested for data-driven uncertainty quantification based on a benchmark scenario of carbon dioxide storage. In the benchmark, for which we provide data and code, carbon dioxide is injected into a saline aquifer modeled by the nonlinear capillarity-free fractional flow formulation for two incompressible fluid phases, namely carbon dioxide and brine. To cover different aspects of uncertainty quantification, we incorporate various sources of uncertainty such as uncertainty of boundary conditions, of conceptual model definitions and of material properties. We consider recent versions of the following non-intrusive and intrusive uncertainty quantification methods: arbitary polynomial chaos, spatially adaptive sparse grids, kernel-based greedy interpolation and hybrid stochastic Galerkin. The performance of each approach is demonstrated assessing expectation value and standard deviation of the carbon dioxide saturation against a reference statistic based on Monte Carlo sampling. We compare the convergence of all methods reporting on accuracy with respect to the number of model runs and resolution. Finally we offer suggestions about the methodsâ€™ advantages and disadvantages that can guide the modeler for uncertainty quantification in carbon dioxide storage and beyond.}, author = {K{\"o}ppel, M. and Franzelin, F. and Kr{\"o}ker, I. and Oladyshkin, S. and Santin, G. and Wittwar, D. and Barth, A. and Haasdonk, Bernard and Nowak, W. and Pfl{\"u}ger, D. and Rohde, C.}, groups = {haasdonk, santin}, institution = {University of Stuttgart}, owner = {santinge}, title = {Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1759}, year = 2017 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1759
9. M. Köppel et al., “Datasets and executables of data-driven uncertainty quantification benchmark in carbon dioxide storage.” Nov. 2017. doi: 10.5281/zenodo.933827.
  - BibTeX
  - Link
  BibTeX
  @misc{UQ_comparison_dataset, author = {K{\"o}ppel, Markus and Franzelin, Fabian and Kr{\"o}ker, Ilja and Oladyshkin, Sergey and Wittwar, Dominik and Santin, Gabriele and Barth, Andrea and Haasdonk, Bernard and Nowak, Wolfang and Pfl{\"u}ger, Dirk and Rohde, Christian}, doi = {10.5281/zenodo.933827}, month = {11}, owner = {santinge}, title = {{Datasets and executables of data-driven uncertainty quantification benchmark in carbon dioxide storage}}, url = {https://doi.org/10.5281/zenodo.933827}, year = 2017 }
  Link
  https://doi.org/10.5281/zenodo.933827
10. T. Köppl, G. Santin, B. Haasdonk, and R. Helmig, “Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods,” University of Stuttgart, 2017.
  - BibTeX
  BibTeX
  @techreport{Koeppl2017, __markedentry = {[haasdonk:6]}, author = {K{\"o}ppl, Tobias and Santin, Gabriele and Haasdonk, Bernard and Helmig, Reiner}, institution = {University of Stuttgart}, owner = {santinge}, title = {Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods}, year = 2017 }
11. I. Martini, G. Rozza, and B. Haasdonk, “Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models,” Journal of Scientific Computing, vol. 74, no. 1, Art. no. 1, Jan. 2017, doi: 10.1007/s10915-017-0430-y.
  - BibTeX
  - Link
  BibTeX
  @article{Martini2015, author = {Martini, I. and Rozza, G. and Haasdonk, Bernard}, doi = {10.1007/s10915-017-0430-y}, file = {:PDF/Martini2015_www_RB_viscous_inviscid_coupling.pdf:PDF}, groups = {haasdonk, maieril, haasdonk_misc, haasdonk_all_papers}, journal = {Journal of Scientific Computing}, month = {01}, number = 1, owner = {maieril}, pages = {197--219}, title = {Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models}, url = {http://link.springer.com/article/10.1007/s10915-017-0430-y}, volume = 74, year = 2017 }
  Link
  http://link.springer.com/article/10.1007/s10915-017-0430-y
12. G. Santin and B. Haasdonk, “Convergence rate of the data-independent P-greedy algorithm in kernel-based approximation,” Dolomites Res. Notes Approx., vol. 10, pp. 68--78, 2017, [Online]. Available: /brokenurl#www.emis.de/journals/DRNA/9-2.html
  - BibTeX
  - Link
  BibTeX
  @article{SH16b, abstract = {Kernel-based methods provide flexible and accurate algorithms for the reconstruction of functions from meshless samples. A major question in the use of such methods is the influence of the samplesâ€™ locations on the behavior of the approximation, and feasible optimal strategies are not known for general problems. Nevertheless, efficient and greedy point-selection strategies are known. This paper gives a proof of the convergence rate of the data-independent $P$-greedy algorithm, based on the application of the convergence theory for greedy algorithms in reduced basis methods. The resulting rate of convergence is shown to be quasi-optimal in the case of kernels generating Sobolev spaces. As a consequence, this convergence rate proves that, for kernels of Sobolev spaces, the points selected by the algorithm are asymptotically uniformly distributed, as conjectured in the paper where the algorithm has been introduced}, author = {Santin, G. and Haasdonk, Bernard}, file = {:PDF/SH16b_www_p-greedy.pdf:PDF}, fjournal = {Dolomites Research Notes on Approximation}, groups = {haasdonk, santin, haasdonk_misc, haasdonk_all_papers}, journal = {Dolomites Res. Notes Approx.}, owner = {haasdonk}, pages = {68--78}, sjournal = {Dolomites Res.\ Notes Approx.}, title = {Convergence rate of the data-independent {P}-greedy algorithm in kernel-based approximation}, url = {/brokenurl#www.emis.de/journals/DRNA/9-2.html}, volume = 10, year = 2017 }
  Link
  /brokenurl#www.emis.de/journals/DRNA/9-2.html
13. G. Santin and B. Haasdonk, “Greedy Kernel Approximation for Sparse Surrogate Modelling,” University of Stuttgart, 2017.
  - BibTeX
  BibTeX
  @techreport{SH2017a, author = {Santin, G. and Haasdonk, Bernard}, institution = {University of Stuttgart}, owner = {santinge}, title = {Greedy Kernel Approximation for Sparse Surrogate Modelling}, year = 2017 }
14. G. Santin and B. Haasdonk, “Non-symmetric kernel greedy interpolation.,” 2017.
  - BibTeX
  BibTeX
  @unpublished{HaSa2017, author = {Santin, G. and Haasdonk, Bernard}, note = {University of Stuttgart, in preparation, 2017.}, owner = {santinge}, title = {Non-symmetric kernel greedy interpolation.}, year = 2017 }
15. A. Schmidt and B. Haasdonk, “Data-driven surrogates of value functions and applications to feedback control for dynamical systems,” University of Stuttgart, 2017. [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1766
  - BibTeX
  - Link
  BibTeX
  @techreport{SH17b, author = {Schmidt, A. and Haasdonk, Bernard}, groups = {haasdonk, schmidta, haasdonk_all_papers}, institution = {University of Stuttgart}, note = {Submitted to MathMod 2018}, owner = {schmidta}, title = {Data-driven surrogates of value functions and applications to feedback control for dynamical systems}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1766}, year = 2017 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1766
16. A. Schmidt and B. Haasdonk, “Reduced basis approximation of large scale parametric algebraic Riccati equations,” ESAIM: Control, Optimisation and Calculus of Variations, Feb. 2017, doi: 10.1051/cocv/2017011.
  - BibTeX
  - Link
  BibTeX
  @article{schmidt2017reduced, author = {Schmidt, Andreas and Haasdonk, Bernard}, doi = {10.1051/cocv/2017011}, issn = {1262-3377}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, month = {02}, owner = {schmidta}, publisher = {EDP Sciences}, title = {Reduced basis approximation of large scale parametric algebraic {Riccati} equations}, url = {http://dx.doi.org/10.1051/cocv/2017011}, year = 2017 }
  Link
  http://dx.doi.org/10.1051/cocv/2017011
17. P. Tempel, A. Schmidt, B. Haasdonk, and A. Pott, “Application of the Rigid Finite Element Method to the Simulation of Cable-Driven Parallel Robots,” in Computational Kinematics, Springer International Publishing, 2017, pp. 198--205. doi: 10.1007/978-3-319-60867-9_23.
  - BibTeX
  - Link
  BibTeX
  @incollection{tempel2017application, author = {Tempel, Philipp and Schmidt, Andreas and Haasdonk, Bernard and Pott, Andreas}, booktitle = {Computational Kinematics}, doi = {10.1007/978-3-319-60867-9_23}, month = {07}, owner = {schmidta}, pages = {198--205}, publisher = {Springer International Publishing}, title = {Application of the Rigid Finite Element Method to the Simulation of Cable-Driven Parallel Robots}, url = {https://doi.org/10.1007%2F978-3-319-60867-9_23}, year = 2017 }
  Link
  https://doi.org/10.1007%2F978-3-319-60867-9_23
18. D. Wittwar, G. Santin, and B. Haasdonk, “Interpolation with uncoupled separable matrix-valued kernels.,” ArXiv preprint 1807.09111, Accepted for publications in Dolomites Res. Notes Approx., 2017.
  - BibTeX
  BibTeX
  @techreport{WSH17a, author = {Wittwar, D. and Santin, G. and Haasdonk, Bernard}, file = {:PDF/WSH17a_uncoupled_MVK.pdf:PDF}, owner = {wittwar}, title = {Interpolation with uncoupled separable matrix-valued kernels.}, type = {ArXiv preprint 1807.09111, Accepted for publications in {Dolomites Res. Notes Approx.}}, year = 2017 }
19. D. Wittwar and B. Haasdonk, “On uncoupled separable matrix-valued kernels,” University of Stuttgart, 2017.
  - BibTeX
  BibTeX
  @techreport{WH17, author = {Wittwar, D. and Haasdonk, Bernard}, institution = {University of Stuttgart}, note = {In preperation}, owner = {wittwar}, title = {On uncoupled separable matrix-valued kernels}, year = 2017 }
20. D. Wittwar, A. Schmidt, and B. Haasdonk, “Reduced Basis Approximation for the Discrete-time Parametric Algebraic Riccati Equation,” University of Stuttgart, 2017.
  - BibTeX
  BibTeX
  @techreport{wittwar2017reduced, author = {Wittwar, D. and Schmidt, A. and Haasdonk, B.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/WSH17_www.pdf:PDF}, institution = {University of Stuttgart}, owner = {schmidta}, title = {Reduced Basis Approximation for the Discrete-time Parametric Algebraic {R}iccati Equation}, year = 2017 }
2016
1. A. Alla, A. Schmidt, and B. Haasdonk, “Model order reduction approaches for infinite horizon optimal control problems via the HJB equation,” University of Stuttgart, Jul. 2016. [Online]. Available: https://arxiv.org/abs/1607.02337
  - BibTeX
  - Link
  BibTeX
  @techreport{ASH16, abstract = {We investigate feedback control for infinite horizon optimal control problems for partial differential equations. The method is based on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is well-known that HJB equations suffer the so called curse of dimensionality and, therefore, a reduction of the dimension of the system is mandatory. In this report we focus on the infinite horizon optimal control problem with quadratic cost functionals. We compare several model reduction methods such as Proper Orthogonal Decomposition, Balanced Truncation and a new algebraic Riccati equation based approach. Finally, we present numerical examples and discuss several features of the different methods analyzing advantages and disadvantages of the reduction methods.}, author = {Alla, Alessandro and Schmidt, Andreas and Haasdonk, Bernard}, eprint = {1607.02337}, file = {:PDF/ASH16_www.pdf:PDF}, groups = {haasdonk_all_papers}, institution = {University of Stuttgart}, month = {07}, note = {Accepted for publication in MoRePaS 2015 Special Issue}, oai2identifier = {1607.02337}, owner = {schmidta}, title = {Model order reduction approaches for infinite horizon optimal control problems via the {HJB} equation}, url = {https://arxiv.org/abs/1607.02337}, year = 2016 }
  Link
  https://arxiv.org/abs/1607.02337
2. D. Amsallem and B. Haasdonk, “PEBL-ROM: Projection-Error Based Local Reduced-Order Models,” AMSES, Advanced Modeling and Simulation in Engineering Sciences, vol. 3, no. 6, Art. no. 6, 2016, doi: 10.1186/s40323-016-0059-7.
  - BibTeX
  - Link
  BibTeX
  @article{AH16, author = {Amsallem, D. and Haasdonk, Bernard}, doi = {10.1186/s40323-016-0059-7}, groups = {haasdonk, haasdonk_all_papers}, journal = {AMSES, Advanced Modeling and Simulation in Engineering Sciences}, number = 6, title = {{PEBL-ROM}: Projection-Error Based Local Reduced-Order Models}, url = {https://amses-journal.springeropen.com/articles/10.1186/s40323-016-0059-7}, volume = 3, year = 2016 }
  Link
  https://amses-journal.springeropen.com/articles/10.1186/s40323-016-0059-7
3. A. C. Antoulas, B. Haasdonk, and B. Peherstorfer, MORML 2016 Book of Abstracts. University of Stuttgart, 2016.
  - BibTeX
  BibTeX
  @book{AHP16, author = {Antoulas, A. C. and Haasdonk, Bernard and Peherstorfer, B.}, groups = {haasdonk, haasdonk_all_papers}, owner = {haasdonk}, publisher = {University of Stuttgart}, title = {MORML 2016 Book of Abstracts}, year = 2016 }
4. U. Baur, P. Benner, B. Haasdonk, C. Himpe, I. Maier, and M. Ohlberger, “Comparison of methods for parametric model order reduction of instationary problems,” in Model Reduction and Approximation for Complex Systems, P. Benner, A. Cohen, M. Ohlberger, and K. Willcox, Eds. Birkhäuser Publishing, 2016. [Online]. Available: https://www2.mpi-magdeburg.mpg.de/preprints/2015/MPIMD15-01.pdf
  - BibTeX
  - Link
  BibTeX
  @incollection{baur2016comparison, author = {Baur, U. and Benner, P. and Haasdonk, B. and Himpe, C. and Maier, I. and Ohlberger, M.}, booktitle = {Model Reduction and Approximation for Complex Systems}, editor = {Benner, P. and Cohen, A. and Ohlberger, M. and Willcox, K.}, owner = {haasdonk}, publisher = {Birkh{\"a}user Publishing}, title = {Comparison of methods for parametric model order reduction of instationary problems}, url = {https://www2.mpi-magdeburg.mpg.de/preprints/2015/MPIMD15-01.pdf}, year = 2016 }
  Link
  https://www2.mpi-magdeburg.mpg.de/preprints/2015/MPIMD15-01.pdf
5. M. Dihlmann and B. Haasdonk, “A REDUCED BASIS KALMAN FILTER FOR PARAMETRIZED PARTIAL DIFFERENTIAL EQUATIONS,” ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, vol. 22, no. 3, Art. no. 3, Jul. 2016, doi: 10.1051/cocv/2015019.
  - BibTeX
  BibTeX
  @article{dihlmann2016reduced, affiliation = {Dihlmann, M (Reprint Author), Univ Stuttgart, Inst Appl Anal \& Numer Simulat, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Dihlmann, Markus; Haasdonk, Bernard, Univ Stuttgart, Inst Appl Anal \& Numer Simulat, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.}, author = {Dihlmann, Markus and Haasdonk, Bernard}, doi = {10.1051/cocv/2015019}, eissn = {1262-3377}, issn = {1292-8119}, journal = {ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS}, language = {English}, month = {07}, number = 3, pages = {625-669}, publisher = {EDP SCIENCES S A}, research-areas = {Automation \& Control Systems; Mathematics}, title = {A REDUCED BASIS KALMAN FILTER FOR PARAMETRIZED PARTIAL DIFFERENTIAL EQUATIONS}, type = {Article}, unique-id = {ISI:000379612000002}, volume = 22, year = 2016 }
6. F. Fritzen, B. Haasdonk, D. Ryckelynck, and S. Schöps, “An algorithmic comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a nonlinear thermal problem,” University of Stuttgart, Arxiv Report, 2016. [Online]. Available: https://arxiv.org/abs/1610.05029
  - BibTeX
  - Link
  BibTeX
  @techreport{FHRS16, author = {Fritzen, Felix and Haasdonk, Bernard and Ryckelynck, David and Sch{\"o}ps, Sebastian}, file = {:PDF/FHRS16_www_CoSiMoR_Preprint_2016.pdf:PDF}, groups = {haasdonk_misc, haasdonk_all_papers}, institution = {University of Stuttgart}, owner = {haasdonk}, title = {An algorithmic comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a nonlinear thermal problem}, type = {Arxiv Report}, url = {https://arxiv.org/abs/1610.05029}, year = 2016 }
  Link
  https://arxiv.org/abs/1610.05029
7. D. Garmatter, B. Haasdonk, and B. Harrach, “A reduced Landweber Method for Nonlinear Inverse Problems,” Inverse Problems, vol. 32, no. 3, Art. no. 3, 2016, doi: http://dx.doi.org/10.1088/0266-5611/32/3/035001.
  - BibTeX
  BibTeX
  @article{GHH16, author = {Garmatter, D. and Haasdonk, Bernard and Harrach, B.}, doi = {http://dx.doi.org/10.1088/0266-5611/32/3/035001}, groups = {haasdonk, haasdonk_all_papers}, journal = {Inverse Problems}, number = 3, pages = {1--21}, title = {A reduced {L}andweber Method for Nonlinear Inverse Problems}, volume = 32, year = 2016 }
8. M. Redeker and B. Haasdonk, “A POD-EIM reduced two-scale model for precipitation in porous media,” MCMDS, Mathematical and Computer Modelling of Dynamical Systems, vol. 22, no. 4, Art. no. 4, 2016, doi: 10.1080/13873954.2016.1198384.
  - BibTeX
  - Link
  BibTeX
  @article{RH2016, author = {Redeker, Magnus and Haasdonk, Bernard}, doi = {10.1080/13873954.2016.1198384}, groups = {haasdonk, haasdonk_all_papers}, journal = {MCMDS, Mathematical and Computer Modelling of Dynamical Systems}, number = 4, pages = {323--344}, title = {A {POD-EIM} reduced two-scale model for precipitation in porous media}, url = {http://www.tandfonline.com/doi/full/10.1080/13873954.2016.1198384}, volume = 22, year = 2016 }
  Link
  http://www.tandfonline.com/doi/full/10.1080/13873954.2016.1198384
9. A. Schmidt and B. Haasdonk, “Reduced basis method for H2 optimal feedback control problems,” IFAC-PapersOnLine, vol. 49, no. 8, Art. no. 8, 2016, doi: http://dx.doi.org/10.1016/j.ifacol.2016.07.462.
  - BibTeX
  - Link
  BibTeX
  @article{SH16, abstract = {Abstract In this paper we examine the application of recently introduced parametric model reduction techniques to the \{H2\} optimal feedback control problem. The \{H2\} control problem provides a realistic framework for control applications, since it considers disturbances in the system and in the measurement outputs. Furthermore it employs state-estimation to reconstruct the unknown state from the noisy measurements. It turns out, that the controller is a dynamical system and two solutions of algebraic Riccati equations (AREs) are required to form it. We apply parametric model order reduction techniques to the \{AREs\} and to the state equation of the observer and show by numerical examples, that this approach can yield a significant speed-up in multi-query scenarios for large scale parametric problems for the control of partial differential equations (PDE).}, author = {Schmidt, A. and Haasdonk, Bernard}, doi = {http://dx.doi.org/10.1016/j.ifacol.2016.07.462}, file = {:PDF/SH16.pdf:PDF}, groups = {haasdonk, schmidta, haasdonk_all_papers}, issn = {2405-8963}, journal = {IFAC-PapersOnLine}, note = {2nd {IFAC} Workshop on Control of Systems Governed by Partial Differential Equations {CPDE} 2016}, number = 8, owner = {schmidta}, pages = {327 - 332}, title = {Reduced basis method for {H2} optimal feedback control problems}, url = {http://www.sciencedirect.com/science/article/pii/S240589631630670X}, volume = 49, year = 2016 }
  Link
  http://www.sciencedirect.com/science/article/pii/S240589631630670X
2015
1. D. Amsallem and B. Haasdonk, “PEBL-ROM: Projection-Error Based Local Reduced-Order Models,” University of Stuttgart, SimTech Preprint, Oct. 2015. [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1436
  - BibTeX
  - Link
  BibTeX
  @techreport{AH15, author = {Amsallem, D. and Haasdonk, Bernard}, institution = {University of Stuttgart}, month = {10}, note = {Submitted to AMSES}, owner = {haasdonk}, title = {PEBL-ROM: Projection-Error Based Local Reduced-Order Models}, type = {SimTech Preprint}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1436}, year = 2015 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1436
2. D. Amsallem, C. Farhat, and B. Haasdonk, “Editorial: Special Issue on Model Reduction,” IJNME, International Journal of Numerical Methods in Engineering, vol. 102, no. 5, Art. no. 5, 2015, doi: 10.1002/nme.4889.
  - BibTeX
  BibTeX
  @article{AFH15, author = {Amsallem, D. and Farhat, C. and Haasdonk, Bernard}, doi = {10.1002/nme.4889}, groups = {haasdonk, haasdonk_all_papers}, journal = {IJNME, International Journal of Numerical Methods in Engineering}, number = 5, owner = {haasdonk}, pages = {931--932}, title = {Editorial: Special Issue on Model Reduction}, volume = 102, year = 2015 }
3. D. Amsallem, C. Farhat, and B. Haasdonk, “Special Issue on Model Reduction,” IJNME, International Journal of Numerical Methods in Engineering, vol. 102, no. 5, Art. no. 5, 2015, doi: 10.1002/nme.4889.
  - BibTeX
  - Link
  BibTeX
  @article{amsallem2015special, author = {Amsallem, D. and Farhat, C. and Haasdonk, B.}, doi = {10.1002/nme.4889}, journal = {IJNME, International Journal of Numerical Methods in Engineering}, number = 5, owner = {haasdonk}, pages = {931--932}, title = {Special Issue on Model Reduction}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.4889}, volume = 102, year = 2015 }
  Link
  https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.4889
4. O. Burkovska, B. Haasdonk, J. Salomon, and B. Wohlmuth, “Reduced basis methods for pricing options with the Black-Scholes and Heston model,” SIAM journal on Financial Mathematics (SIFIN), vol. 6, no. 1, Art. no. 1, 2015, doi: 10.1137/140981216.
  - BibTeX
  BibTeX
  @article{Burkovska2015, author = {Burkovska, O. and Haasdonk, Bernard and Salomon, J. and Wohlmuth, B.}, doi = {10.1137/140981216}, groups = {haasdonk, haasdonk_all_papers}, journal = {SIAM journal on Financial Mathematics (SIFIN)}, number = 1, pages = {685--712}, title = {Reduced basis methods for pricing options with the {B}lack-{S}choles and {H}eston model}, volume = 6, year = 2015 }
5. M. Dihlmann and B. Haasdonk, “A reduced basis Kalman filter for parametrized partial differential equations,” ESAIM: Control, Optimisation and Calculus of Variations, 2015, doi: 10.1051/cocv/2015019.
  - BibTeX
  - Link
  BibTeX
  @article{dihlmann2015reduced, author = {Dihlmann, M. and Haasdonk, B.}, doi = {10.1051/cocv/2015019}, journal = {{ESAIM}: Control, Optimisation and Calculus of Variations}, owner = {schmidta}, publisher = {{EDP} Sciences}, qualityassured = {qualityAssured}, title = {A reduced basis {K}alman filter for parametrized partial differential equations}, url = {http://dx.doi.org/10.1051/cocv/2015019}, year = 2015 }
  Link
  http://dx.doi.org/10.1051/cocv/2015019
6. M. A. Dihlmann and B. Haasdonk, “Certified PDE-constrained parameter optimization using reduced basis surrogate models for evolution problems,” COAP, Computational Optimization and Applications, vol. 60, no. 3, Art. no. 3, 2015, doi: DOI: 10.1007/s10589-014-9697-1.
  - BibTeX
  BibTeX
  @article{Dihlmann2014a, author = {Dihlmann, M. A. and Haasdonk, Bernard}, doi = {DOI: 10.1007/s10589-014-9697-1}, file = {:PDF/Dihlmann2014a.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, journal = {COAP, Computational Optimization and Applications}, number = 3, owner = {dihlmann}, pages = {753--787}, title = {Certified {PDE}-constrained parameter optimization using reduced basis surrogate models for evolution problems}, volume = 60, year = 2015 }
7. D. Garmatter, B. Haasdonk, and B. Harrach, “A reduced Landweber Method for Nonlinear Inverse Problems,” University of Stuttgart, 2015.
  - BibTeX
  BibTeX
  @techreport{GHH15, author = {Garmatter, D. and Haasdonk, Bernard and Harrach, B.}, institution = {University of Stuttgart}, note = {Available at Arxiv}, owner = {haasdonk}, title = {A reduced {L}andweber Method for Nonlinear Inverse Problems}, year = 2015 }
8. S. Kaulmann, B. Flemisch, B. Haasdonk, K.-A. Lie, and M. Ohlberger, “The Localized Reduced Basis Multiscale method for two-phase flows in porous media,” Internat. J. Numer. Methods Engrg., vol. 102, pp. 1018--1040, 2015, doi: DOI: 10.1002/nme.4773.
  - BibTeX
  BibTeX
  @article{kaulmann2015localized, author = {Kaulmann, Sven and Flemisch, Bernd and Haasdonk, Bernard and Lie, Knut-Andreas and Ohlberger, Mario}, doi = {DOI: 10.1002/nme.4773}, journal = {Internat. J. Numer. Methods Engrg.}, owner = {haasdonk}, pages = {1018--1040}, title = {{The Localized Reduced Basis Multiscale method for two-phase flows in porous media}}, volume = 102, year = 2015 }
9. I. Martini and B. Haasdonk, “Output Error Bounds for the Dirichlet-Neumann Reduced Basis Method,” in Numerical Mathematics and Advanced Applications - ENUMATH 2013, 2015, vol. 103, pp. 437--445. doi: 10.1007/978-3-319-10705-9_43.
  - BibTeX
  - Link
  BibTeX
  @inproceedings{Maier2013a, author = {Martini, I. and Haasdonk, Bernard}, booktitle = {Numerical Mathematics and Advanced Applications - ENUMATH 2013}, doi = {10.1007/978-3-319-10705-9_43}, file = {:PDF/Maier2013a_www_RB_homogeneous_DD_output_bounds.pdf:PDF}, groups = {haasdonk, maieril, haasdonk_all_papers}, owner = {maieril}, pages = {437--445}, series = {Lecture Notes in Computational Science and Engineering}, title = {Output Error Bounds for the {D}irichlet-{N}eumann Reduced Basis Method}, url = {http://link.springer.com/chapter/10.1007%2F978-3-319-10705-9_43}, volume = 103, year = 2015 }
  Link
  http://link.springer.com/chapter/10.1007%2F978-3-319-10705-9_43
10. I. Martini, G. Rozza, and B. Haasdonk, “Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system,” Advances in Computational Mathematics, vol. 41, no. 5, Art. no. 5, 2015, doi: 10.1007/s10444-014-9396-6.
  - BibTeX
  - Link
  BibTeX
  @article{Maier2014a, author = {Martini, I. and Rozza, G. and Haasdonk, Bernard}, doi = {10.1007/s10444-014-9396-6}, file = {:PDF/Maier2014a_www_RB_stokes_darcy_preprint.pdf:PDF}, groups = {haasdonk, maieril, haasdonk_all_papers}, journal = {Advances in Computational Mathematics}, number = 5, owner = {maieril}, pages = {1131--1157}, title = {Reduced basis approximation and a-posteriori error estimation for the coupled {S}tokes-{D}arcy system}, url = {http://link.springer.com/article/10.1007/s10444-014-9396-6}, volume = 41, year = 2015 }
  Link
  http://link.springer.com/article/10.1007/s10444-014-9396-6
11. M. Redeker and B. Haasdonk, “A POD-EIM reduced two-scale model for precipitation in porous media,” University of Stuttgart, SimTech Preprint, 2015. [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=964
  - BibTeX
  - Link
  BibTeX
  @techreport{Redeker2015, author = {Redeker, Magnus and Haasdonk, Bernard}, institution = {University of Stuttgart}, owner = {haasdonk}, title = {A {POD-EIM} reduced two-scale model for precipitation in porous media}, type = {SimTech Preprint}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=964}, year = 2015 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=964
12. M. Redeker and B. Haasdonk, “A POD-EIM reduced two-scale model for crystal growth,” ADVANCES IN COMPUTATIONAL MATHEMATICS, vol. 41, no. 5, SI, Art. no. 5, SI, Oct. 2015, doi: 10.1007/s10444-014-9367-y.
  - BibTeX
  BibTeX
  @article{redeker2015podeim, affiliation = {Redeker, M (Reprint Author), Univ Stuttgart, Inst Appl Anal \& Numer Simulat, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Redeker, Magnus; Haasdonk, Bernard, Univ Stuttgart, Inst Appl Anal \& Numer Simulat, D-70569 Stuttgart, Germany.}, author = {Redeker, Magnus and Haasdonk, Bernard}, doi = {10.1007/s10444-014-9367-y}, eissn = {1572-9044}, issn = {1019-7168}, journal = {ADVANCES IN COMPUTATIONAL MATHEMATICS}, language = {English}, month = {10}, number = {5, SI}, pages = {987-1013}, publisher = {SPRINGER}, research-areas = {Mathematics}, title = {A POD-EIM reduced two-scale model for crystal growth}, type = {Article}, unique-id = {ISI:000365740300003}, volume = 41, year = 2015 }
13. A. Schmidt, M. Dihlmann, and B. Haasdonk, “Basis generation approaches for a reduced basis linear quadratic regulator,” in Proc. MATHMOD 2015 - 8th Vienna International Conference on Mathematical Modelling, 2015, pp. 713--718. doi: 10.1016/j.ifacol.2015.05.016.
  - BibTeX
  - Link
  BibTeX
  @inproceedings{SDH14, author = {Schmidt, A. and Dihlmann, M. and Haasdonk, Bernard}, booktitle = {Proc. MATHMOD 2015 - 8th Vienna International Conference on Mathematical Modelling}, doi = {10.1016/j.ifacol.2015.05.016}, groups = {haasdonk, schmidta, haasdonk_all_papers}, owner = {schmidta}, pages = {713--718}, title = {Basis generation approaches for a reduced basis linear quadratic regulator}, url = {http://dx.doi.org/10.1016/j.ifacol.2015.05.016}, year = 2015 }
  Link
  http://dx.doi.org/10.1016/j.ifacol.2015.05.016
14. A. Schmidt and B. Haasdonk, “Reduced basis method for $H_2$ optimal feedback control problems,” University of Stuttgart, 2015. [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1442
  - BibTeX
  - Link
  BibTeX
  @techreport{SH15a, author = {Schmidt, A. and Haasdonk, Bernard}, institution = {University of Stuttgart}, owner = {schmidta}, title = {Reduced basis method for $\mathcal{H}_2$ optimal feedback control problems}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1442}, year = 2015 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1442
15. A. Schmidt and B. Haasdonk, “Reduced Basis Approximation of Large Scale Algebraic Riccati Equations,” University of Stuttgart, 2015.
  - BibTeX
  BibTeX
  @techreport{SH15, author = {Schmidt, A. and Haasdonk, Bernard}, institution = {University of Stuttgart}, note = {Submitted}, owner = {schmidta}, title = {Reduced Basis Approximation of Large Scale Algebraic {R}iccati Equations}, year = 2015 }
16. D. Wirtz, N. Karajan, and B. Haasdonk, “Surrogate Modelling of multiscale models using kernel methods,” International Journal of Numerical Methods in Engineering, vol. 101, no. 1, Art. no. 1, 2015, doi: 10.1002/nme.4767.
  - BibTeX
  BibTeX
  @article{wirtz2015surrogate, author = {Wirtz, D. and Karajan, N. and Haasdonk, B.}, doi = {10.1002/nme.4767}, journal = {International Journal of Numerical Methods in Engineering}, number = 1, owner = {haasdonk}, pages = {1--28}, title = {Surrogate Modelling of multiscale models using kernel methods}, volume = 101, year = 2015 }
17. D. Wirtz, N. Karajan, and B. Haasdonk, “Surrogate modeling of multiscale models using kernel methods,” INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, vol. 101, no. 1, Art. no. 1, Jan. 2015, doi: 10.1002/nme.4767.
  - BibTeX
  BibTeX
  @article{wirtz2015surrogate, affiliation = {Wirtz, D (Reprint Author), Univ Stuttgart, Inst Appl Mech CE, Pfaffenwaldring 5a, D-70569 Stuttgart, Germany. Wirtz, D., Univ Stuttgart, Inst Appl Mech CE, D-70569 Stuttgart, Germany. Karajan, N., DYNAmore GmbH, D-70565 Stuttgart, Germany. Haasdonk, B., Univ Stuttgart, Inst Appl Anal \& Numer Simulat, D-70569 Stuttgart, Germany.}, author = {Wirtz, Daniel and Karajan, N. and Haasdonk, Bernard}, doi = {10.1002/nme.4767}, eissn = {1097-0207}, issn = {0029-5981}, journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING}, language = {English}, month = {01}, number = 1, pages = {1-28}, publisher = {WILEY-BLACKWELL}, research-areas = {Engineering; Mathematics}, title = {Surrogate modeling of multiscale models using kernel methods}, type = {Article}, unique-id = {ISI:000345824800001}, volume = 101, year = 2015 }
2014
1. O. Burkovska, B. Haasdonk, J. Salomon, and B. Wohlmuth, “Reduced basis methods for pricing options with the Black-Scholes and Heston model,” Arxiv, Preprint 1408.1220, 2014. [Online]. Available: http://arxiv.org/abs/1408.1220
  - BibTeX
  - Link
  BibTeX
  @techreport{Burkovska2014, author = {Burkovska, O. and Haasdonk, Bernard and Salomon, J. and Wohlmuth, B.}, institution = {Arxiv}, number = {1408.1220}, owner = {haasdonk}, title = {Reduced basis methods for pricing options with the {B}lack-{S}choles and {H}eston model}, type = {Preprint}, url = {http://arxiv.org/abs/1408.1220}, year = 2014 }
  Link
  http://arxiv.org/abs/1408.1220
2. M. Dihlmann and B. Haasdonk, “A reduced basis Kalman filter for parametrized partial differential equations,” University of Stuttgart, 2014.
  - BibTeX
  BibTeX
  @techreport{Dihlmann2014, author = {Dihlmann, M. and Haasdonk, Bernard}, file = {:PDF/Dihlmann2014a.pdf:PDF}, institution = {University of Stuttgart}, note = {Submitted to ESAIM: COCV}, owner = {dihlmann}, title = {A reduced basis Kalman filter for parametrized partial differential equations}, year = 2014 }
3. B. Haasdonk and M. Ohlberger, “Wenn die Probleme zahlreicher werden: Reduzierte Basis Methoden f�r effiziente und gesicherte numerische Simulation,” GAMM Rundbrief, vol. 2014, no. 1, Art. no. 1, 2014.
  - BibTeX
  BibTeX
  @article{haasdonk2014probleme, author = {Haasdonk, B. and Ohlberger, M.}, journal = {GAMM Rundbrief}, number = 1, owner = {haasdonk}, pages = {6-13}, title = {Wenn die {P}robleme zahlreicher werden: {R}eduzierte {B}asis {M}ethoden f�r effiziente und gesicherte numerische {S}imulation}, volume = 2014, year = 2014 }
4. B. Haasdonk and M. Ohlberger, “Wenn die Probleme zahlreicher werden: Reduzierte Basis Methoden für effiziente und gesicherte numerische Simulation,” GAMM Rundbrief, vol. 2014, no. 1, Art. no. 1, 2014.
  - BibTeX
  BibTeX
  @article{Haasdonk2014, author = {Haasdonk, Bernard and Ohlberger, M.}, groups = {haasdonk, haasdonk_all_papers}, journal = {GAMM Rundbrief}, number = 1, owner = {haasdonk}, pages = {6-13}, title = {Wenn die {P}robleme zahlreicher werden: {R}eduzierte {B}asis {M}ethoden f{\"u}r effiziente und gesicherte numerische {S}imulation}, volume = 2014, year = 2014 }
5. B. Haasdonk, “Reduced Basis Methods for Parametrized PDEs -- A Tutorial Introduction for Stationary and Instationary Problems,” IANS, University of Stuttgart, Germany, SimTech Preprint, 2014. [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=938
  - BibTeX
  - Link
  BibTeX
  @techreport{Haasdonk2014a, author = {Haasdonk, Bernard}, file = {:PDF/Haasdonk2014a_www_preprint_RBtutorial_with_update2016.pdf:PDF}, groups = {haasdonk_misc, haasdonk_all_papers}, institution = {IANS, University of Stuttgart, Germany}, note = {Chapter in Benner, P., A. Cohen, Ohlberger, M. and K. Willcox (eds.): "Model Reduction and Approximation: Theory and Algorithms", SIAM, Philadelphia, 2017}, owner = {haasdonk}, title = {Reduced Basis Methods for Parametrized {PDE}s -- A Tutorial Introduction for Stationary and Instationary Problems}, type = {{S}im{T}ech Preprint}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=938}, year = 2014 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=938
6. S. Kaulmann, B. Flemisch, B. Haasdonk, K.-A. Lie, and M. Ohlberger, “The localized reduced basis multiscale method for two-phase flows in porous media,” International Journal for Numerical Methods in Engineering, Sep. 2014, doi: 10.1002/nme.4773.
  - BibTeX
  BibTeX
  @article{Kaulmann2014a, author = {Kaulmann, S. and Flemisch, B. and Haasdonk, Bernard and Lie, K.-A. and Ohlberger, M.}, doi = {10.1002/nme.4773}, file = {:PDF/confidential_journal_version_kaulmann_et_al_IJNME_2014.pdf:PDF}, journal = {International Journal for Numerical Methods in Engineering}, month = {09}, owner = {haasdonk}, publisher = {Wiley}, title = {The localized reduced basis multiscale method for two-phase flows in porous media}, year = 2014 }
7. S. Kaulmann, B. Flemisch, B. Haasdonk, K. A. Lie, and M. Ohlberger, “The Localized Reduced Basis Multiscale method for two-phase flow in porous media,” arXiv preprint arXiv:1405.2810, 2014.
  - BibTeX
  BibTeX
  @techreport{Kaulmann2014b, author = {Kaulmann, S. and Flemisch, B. and Haasdonk, Bernard and Lie, K.A. and Ohlberger, M.}, institution = {arXiv preprint arXiv:1405.2810}, owner = {Markus}, title = {The {L}ocalized {R}educed {B}asis {M}ultiscale method for two-phase flow in porous media}, year = 2014 }
8. I. Maier and B. Haasdonk, “A Dirichlet-Neumann reduced basis method for homogeneous domain decomposition problems,” Applied Numerical Mathematics, vol. 78, pp. 31--48, 2014, doi: 10.1016/j.apnum.2013.12.001.
  - BibTeX
  - Link
  BibTeX
  @article{Maier2014, author = {Maier, I. and Haasdonk, Bernard}, doi = {10.1016/j.apnum.2013.12.001}, file = {:PDF/Maier2014_www_preprint_RB_homogeneous_domain_decomposition.pdf:PDF}, groups = {haasdonk, maieril, haasdonk_all_papers}, journal = {Applied Numerical Mathematics}, owner = {maieril}, pages = {31--48}, title = {A {D}irichlet-{N}eumann reduced basis method for homogeneous domain decomposition problems}, url = {http://www.sciencedirect.com/science/article/pii/S0168927413001657}, volume = 78, year = 2014 }
  Link
  http://www.sciencedirect.com/science/article/pii/S0168927413001657
9. D. Wirtz, D. C. Sorensen, and B. Haasdonk, “A-posteriori error estimation for DEIM reduced nonlinear dynamical systems,” SIAM J. Sci. Comp., vol. 36, no. 2, Art. no. 2, 2014, [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=733
  - BibTeX
  - Link
  BibTeX
  @article{wirtz2014aposteriori, abstract = {In this work an effcient approach for a-posteriori error estimation for POD-DEIM reduced nonlinear dynamical systems is introduced. The considered nonlinear systems may also include time and parameter-affne linear terms as well as parametrically dependent inputs and outputs. The reduction process involves a Galerkin projection of the full system and approximation of the system's nonlinearity by the DEIM method [Chaturantabut & Sorensen (2010)]. The proposed a-posteriori error estimator can be effciently decomposed in an offine/online fashion and is obtained by a one dimensional auxiliary ODE during reduced simulations. Key elements for effcient online computation are partial similarity transformations and matrix DEIM approximations of the nonlinearity Jacobians. The theoretical results are illustrated by application to an unsteady Burgers equation and a cell apoptosis model.}, author = {Wirtz, D. and Sorensen, D.C. and Haasdonk, B.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/WSH14_www_WSH12_preprint_version.pdf:PDF}, institution = {University of Stuttgart}, journal = {SIAM J. Sci. Comp.}, number = 2, owner = {haasdonk}, pages = {A311--A338}, title = {A-posteriori error estimation for DEIM reduced nonlinear dynamical systems}, type = {SimTech Preprint}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=733}, volume = 36, year = 2014 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=733
2013
1. D. Amsallem, B. Haasdonk, and G. Rozza, “A Conference within a Conference for MOR Researchers,” SIAM News, vol. 46, no. 6, Art. no. 6, Jul. 2013, [Online]. Available: http://www.siam.org/news/news.php?id=2089
  - BibTeX
  - Link
  BibTeX
  @article{Amsallem2013, author = {Amsallem, D. and Haasdonk, Bernard and Rozza, G.}, groups = {haasdonk, haasdonk_all_papers}, journal = {SIAM News}, month = {07}, number = 6, owner = {haasdonk}, pages = 8, title = {A Conference within a Conference for MOR Researchers}, url = {http://www.siam.org/news/news.php?id=2089}, volume = 46, year = 2013 }
  Link
  http://www.siam.org/news/news.php?id=2089
2. M. Dihlmann and B. Haasdonk, “Certified Nonlinear Parameter Optimization with Reduced Basis Surrogate Models,” PAMM, Proc. Appl. Math. Mech., Special Issue: 84th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Novi Sad 2013; Editors: L. Cvetković, T. Atanacković and V. Kostić, vol. 13, no. 1, Art. no. 1, 2013, doi: doi: 10.1002/pamm.201310002.
  - BibTeX
  BibTeX
  @article{DH13b, author = {Dihlmann, M. and Haasdonk, Bernard}, doi = {doi: 10.1002/pamm.201310002}, groups = {haasdonk, haasdonk_all_papers}, journal = {PAMM, Proc. Appl. Math. Mech., Special Issue: 84th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Novi Sad 2013; Editors: L. Cvetkovi\'{c}, T. Atanackovi\'{c} and V. Kosti\'{c}}, number = 1, owner = {dihlmann}, pages = {3--6}, title = {Certified Nonlinear Parameter Optimization with Reduced Basis Surrogate Models}, volume = 13, year = 2013 }
3. M. A. Dihlmann and B. Haasdonk, “Certified PDE-constrained parameter optimization using reduced basis surrogate models for evolution problems,” University of Stuttgart (The final publication is available at Springer via http://dx.doi.org/10.1007/s10589-014-9697-1), SimTech Preprint, 2013.
  - BibTeX
  BibTeX
  @techreport{dihlmann2013certified, author = {Dihlmann, M. A. and Haasdonk, B.}, file = {:/afs/.mathe/public/www/ians/am/Haasdonk/publications/DH13.pdf:PDF}, institution = {University of Stuttgart (The final publication is available at Springer via http://dx.doi.org/10.1007/s10589-014-9697-1)}, owner = {dihlmann}, title = {Certified PDE-constrained parameter optimization using reduced basis surrogate models for evolution problems}, type = {SimTech Preprint}, year = 2013 }
4. J. Fehr, M. Fischer, B. Haasdonk, and P. Eberhard, “Greedy-based Approximation of Frequency-weighted Gramian Matrices for Model Reduction in Multibody Dynamics,” ZAMM, vol. 93, no. 8, Art. no. 8, 2013, doi: 10.1002/zamm.201200014.
  - BibTeX
  - Link
  BibTeX
  @article{Fehr2013, author = {Fehr, J. and Fischer, M. and Haasdonk, Bernard and Eberhard, P.}, doi = {10.1002/zamm.201200014}, groups = {haasdonk, haasdonk_all_papers}, journal = {ZAMM}, number = 8, owner = {haasdonk}, pages = {501-519}, title = {Greedy-based Approximation of Frequency-weighted Gramian Matrices for Model Reduction in Multibody Dynamics}, url = {http://onlinelibrary.wiley.com/doi/10.1002/zamm.201200014/pdf}, volume = 93, year = 2013 }
  Link
  http://onlinelibrary.wiley.com/doi/10.1002/zamm.201200014/pdf
5. B. Haasdonk, K. Urban, and B. Wieland, “Reduced basis methods for parametrized partial differential equations with stochastic influences using the Karhunen Loeve expansion,” SIAM/ASA J. Unc. Quant., vol. 1, pp. 79–105, 2013.
  - BibTeX
  BibTeX
  @article{Haasdonk2013, author = {Haasdonk, Bernard and Urban, K. and Wieland, B.}, file = {:PDF/Haasdonk2013_www_preprint_HUW2012_RB_stochastic_PDEs.pdf:PDF;:PDF/Haasdonk2013_HUW2013_SIAM_UQ_RB_stochastic_PDEs.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, journal = {SIAM/ASA J. Unc. Quant.}, owner = {haasdonk}, pages = {79-105}, title = {Reduced basis methods for parametrized partial differential equations with stochastic influences using the {K}arhunen {L}oeve expansion}, volume = 1, year = 2013 }
6. B. Haasdonk, “Convergence Rates of the POD--Greedy Method,” ESAIM: Mathematical Modelling and Numerical Analysis, vol. 47, no. 3, Art. no. 3, 2013, doi: 10.1051/m2an/2012045.
  - BibTeX
  - Link
  BibTeX
  @article{H13, abstract = {Iterative approximation algorithms are successfully applied in parametric approximation tasks. In particular, reduced basis methods make use of the so-called Greedy algorithm for approximating solution sets of parametrized partial differential equations. Recently, a-priori convergence rate statements for this algorithm have been given (Buffa et al 2009, Binev et al. 2010). The goal of the current study is the extension to time-dependent problems, which are typically approximated using the POD-Greedy algorithm (Haasdonk and Ohlberger 2008). In this algorithm, each greedy step is invoking a temporal compression step by performing a proper orthogonal decomposition (POD). Using a suitable coefficient representation of the POD-Greedy algorithm, we show that the existing convergence rate results of the Greedy algorithm can be extended. In particular, exponential or algebraic convergence rates of the Kolmogorov n-widths are maintained by the POD-Greedy algorithm.}, author = {Haasdonk, Bernard}, doi = {10.1051/m2an/2012045}, file = {:PDF/H13_www_preprint_POD_Greedy_Convergence.pdf:PDF;:PDF/H13_M2AN_POD_Greedy_Convergence_print_version.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, journal = {{ESAIM}: Mathematical Modelling and Numerical Analysis}, number = 3, owner = {schmidta}, pages = {859--873}, publisher = {{EDP} Sciences}, title = {Convergence Rates of the {POD}--{G}reedy Method}, url = {http://dx.doi.org/10.1051/m2an/2012045}, volume = 47, year = 2013 }
  Link
  http://dx.doi.org/10.1051/m2an/2012045
7. S. Kaulmann and B. Haasdonk, “Online Greedy Reduced Basis Construction using Dictionaries,” University of Stuttgart, SimTech Preprint, 2013.
  - BibTeX
  BibTeX
  @techreport{Kaulmann2013a, author = {Kaulmann, S. and Haasdonk, Bernard}, file = {:PDF/Kaulmann2013a_www_Online_Greedy_preprint.pdf:PDF}, institution = {University of Stuttgart}, note = {Submitted to ADMOS 2013}, owner = {haasdonk}, title = {Online Greedy Reduced Basis Construction using Dictionaries}, type = {SimTech Preprint}, year = 2013 }
8. D. Wirtz and B. Haasdonk, “An Improved Vectorial Kernel Orthogonal Greedy Algorithm,” Dolomites Research Notes on Approximation, vol. 6, pp. 83–100, 2013, [Online]. Available: http://drna.di.univr.it/papers/2013/WirtzHaasdonk.2013.VKO.pdf
  - BibTeX
  - Link
  BibTeX
  @article{wirtz2013improved, abstract = {This work is concerned with derivation and analysis of a modifed vectorial kernel orthogonal greedy algorithm (VKOGA) for approximation of nonlinear vectorial functions. The algorithm pursues simultaneous approximation of all vector components over a shared linear subspace of the underlying function Hilbert space in a greedy fashion [14, 33] and inherits the selection principle of the f=P-Greedy algorithm [18]. For the considered algorithm we perform a limit analysis of the selection criteria for already included subspace basis functions. We show that the approximation gain is bounded globally and for the multivariate case the limit functions correspond to a directional Hermite interpolation. We further prove algebraic convergence similar to [13], improved by a dimension-dependent factor, and introduce a new a-posteriori error bound. Comparison to related variants of our algorithm are presented. Targeted applications of this algorithm are model reduction of multiscale models [40].}, author = {Wirtz, D. and Haasdonk, B.}, file = {:/home/dwirtz/dwirtzwww/WH12c_preprint.pdf:PDF}, journal = {Dolomites Research Notes on Approximation}, owner = {haasdonk}, pages = {83-100}, title = {An Improved Vectorial Kernel Orthogonal Greedy Algorithm}, type = {SimTech Preprint}, url = {http://drna.di.univr.it/papers/2013/WirtzHaasdonk.2013.VKO.pdf}, volume = 6, year = 2013 }
  Link
  http://drna.di.univr.it/papers/2013/WirtzHaasdonk.2013.VKO.pdf
9. D. Wirtz and B. Haasdonk, “A Vectorial Kernel Orthogonal Greedy Algorithm,” Dolomites Res. Notes Approx., vol. 6, pp. 83–100, 2013, [Online]. Available: http://drna.padovauniversitypress.it/system/files/papers/WirtzHaasdonk-2013-VKO.pdf
  - BibTeX
  - Link
  BibTeX
  @article{wirtz2013vectorial, abstract = {This work is concerned with derivation and analysis of a modified vectorial kernel orthogonal greedy algorithm (VKOGA) for approximation of nonlinear vectorial functions. The algorithm pursues sim- ultaneous approximation of all vector components over a shared linear subspace of the underlying function Hilbert space in a greedy fashion [16, 37] and inherits the selection principle of the f /P-Greedy algorithm [20]. For the considered algorithm we perform a limit analysis of the selection criteria for already included subspace basis functions. We show that the approximation gain is bounded globally and for the multivariate case the limit functions correspond to a directional Hermite interpolation. We further prove algebraic convergence similar to [14], improved by a dimension-dependent factor, and introduce a new a-posteriori error bound. Comparison to related variants of our algorithm are presented. Targeted applications of this algorithm are model reduction of multiscale models [42].}, author = {Wirtz, Daniel and Haasdonk, Bernard}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Wirtz2013_www_preprint_vectorial_kernel_orthogonal_greedy_algorithm.pdf:PDF}, fjournal = {Dolomites Research Notes on Approximation}, journal = {Dolomites Res. Notes Approx.}, note = {Proceedings of DWCAA12}, owner = {dwirtz}, pages = {83-100}, sjournal = {Dolomites Res.\ Notes Approx.}, title = {A Vectorial Kernel Orthogonal Greedy Algorithm}, url = {http://drna.padovauniversitypress.it/system/files/papers/WirtzHaasdonk-2013-VKO.pdf}, volume = 6, year = 2013 }
  Link
  http://drna.padovauniversitypress.it/system/files/papers/WirtzHaasdonk-2013-VKO.pdf
2012
1. F. Albrecht, B. Haasdonk, S. Kaulmann, and M. Ohlberger, “The Localized Reduced Basis Multiscale Method,” in ALGORITMY 2012 - Proceedings of contributed papers and posters, Apr. 2012, vol. 1, pp. 393--403. [Online]. Available: http://www.iam.fmph.uniba.sk/algoritmy2012/zbornik/40Albrecht.pdf
  - BibTeX
  - Link
  BibTeX
  @inproceedings{Albrecht2012, author = {Albrecht, F. and Haasdonk, Bernard and Kaulmann, S. and Ohlberger, M.}, bdsk-url-1 = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=698}, booktitle = {ALGORITMY 2012 - Proceedings of contributed papers and posters}, date-added = {2012-07-05 15:58:40 +0200}, date-modified = {2012-10-12 08:59:35 +0000}, editor = {Handlovicova, A. and Minarechova, Z. and Cevcovic, D.}, file = {:PDF/Albrecht2012_www_LRBMS_method_Algoritmy_Proceedings.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, month = {04}, organization = {Slovak University of Technology in Bratislava}, owner = {haasdonk}, pages = {393--403}, preprinturl = {http://wwwmath.uni-muenster.de/num/publications/2012/AHKO12/AHKO12.pdf}, publisher = {Publishing House of STU}, pubtype = {Misc}, title = {The Localized Reduced Basis Multiscale Method}, url = {http://www.iam.fmph.uniba.sk/algoritmy2012/zbornik/40Albrecht.pdf}, volume = 1, year = 2012 }
  Link
  http://www.iam.fmph.uniba.sk/algoritmy2012/zbornik/40Albrecht.pdf
2. M. Dihlmann, S. Kaulmann, and B. Haasdonk, “Online Reduced Basis Construction Procedure for Model Reduction of Parametrized Evolution Systems,” 2012.
  - BibTeX
  BibTeX
  @inproceedings{Dihlmann2012, author = {Dihlmann, M. and Kaulmann, S. and Haasdonk, Bernard}, booktitle = {Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling}, file = {:PDF/Dihlmann2012_www_Mathmod2012_online_greedy_evolution_RB.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, owner = {haasdonk}, title = {Online Reduced Basis Construction Procedure for Model Reduction of Parametrized Evolution Systems}, year = 2012 }
3. M. Drohmann, B. Haasdonk, and M. Ohlberger, “Reduced Basis Model Reduction of Parametrized Two-phase Flow in Porous Media,” 2012. doi: https://doi.org/10.3182/20120215-3-AT-3016.00128.
  - BibTeX
  - Link
  BibTeX
  @inproceedings{Drohmann2012a, author = {Drohmann, M. and Haasdonk, Bernard and Ohlberger, M.}, booktitle = {Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling}, doi = {https://doi.org/10.3182/20120215-3-AT-3016.00128}, file = {:PDF/Drohmann2012a.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, owner = {haasdonk}, title = {Reduced Basis Model Reduction of Parametrized Two-phase Flow in Porous Media}, url = {http://www.sciencedirect.com/science/article/pii/S1474667016307613}, year = 2012 }
  Link
  http://www.sciencedirect.com/science/article/pii/S1474667016307613
4. M. Drohmann, B. Haasdonk, and M. Ohlberger, “Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation,” SIAM J. Sci. Comput., vol. 34, no. 2, Art. no. 2, 2012, doi: 10.1137/10081157X.
  - BibTeX
  BibTeX
  @article{Drohmann2012, abstract = {We present a new approach to treating nonlinear operators in reduced basis approximations of parametrized evolution equations. Our approach is based on empirical interpolation of nonlinear differential operators and their Frechet derivatives. Efficient offline/online decomposition is obtained for discrete operators that allow an efficient evaluation for a certain set of interpolation functionals. An a posteriori error estimate for the resulting reduced basis method is derived and analyzed numerically. We introduce a new algorithm, the PODEI-greedy algorithm, which constructs the reduced basis spaces for the empirical interpolation and for the numerical scheme in a synchronized way. The approach is applied to nonlinear parabolic and hyperbolic equations based on explicit or implicit finite volume discretizations. We show that the resulting reduced scheme is able to capture the evolution of both smooth and discontinuous solutions. In case of symmetries of the problem, the approach realizes an automatic and intuitive space-compression or even space-dimensionality reduction. We perform empirical investigations of the error convergence and run-times. In all cases we obtain a good run-time acceleration.}, author = {Drohmann, M. and Haasdonk, Bernard and Ohlberger, M.}, doi = {10.1137/10081157X}, eprint = {http://epubs.siam.org/doi/pdf/10.1137/10081157X}, file = {:PDF/UNSORTED/DHO12 - RB Approx for nonlin evol.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, journal = {SIAM J. Sci. Comput.}, number = 2, owner = {dwirtz}, pages = {A937-A969}, title = {Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation}, volume = 34, year = 2012 }
5. M. Drohmann, B. Haasdonk, and M. Ohlberger, “A Software Framework for Reduced Basis Methods Using DUNE-RB and RBMATLAB,” in Advances in DUNE: Proceedings of the DUNE User Meeting, Held in October 6th-8th 2010 in Stuttgart, Germany, A. Dedner, B. Flemisch, and R. Klöfkorn, Eds. Springer, 2012. [Online]. Available: http://www.springer.com/engineering/computational+intelligence+and+complexity/book/978-3-642-28588-2
  - BibTeX
  - Link
  BibTeX
  @incollection{drohmann2012software, abstract = {Many applications from science and engineering are based on parametrized evolution equations and depend on time-consuming parameter studies or need to ensure critical constraints on the simulation time. For both settings, model order reduction by the reduced basis approach is a suitable means to reduce computational time. The method is based on a projection of an underlying high dimensional nu- merical scheme onto a low dimensional function space. In this contribution, a new software framework is introduced that allows fast development of reduced schemes for a large class of discretizations of evolution equations implemented in DUNE. The approach provides a strict separation of low-dimensional and high-dimensional computations, each implemented by its own software package RBMATLAB, respectively DUNE-RB. The functionality of the framework is exemplified for a finite volume approximation of an instationary linear convection-diffusion problem.}, author = {Drohmann, Martin and Haasdonk, Bernard and Ohlberger, Mario}, booktitle = {Advances in DUNE: Proceedings of the DUNE User Meeting, Held in October 6th-8th 2010 in Stuttgart, Germany}, date-added = {2012-10-24T14:53:21GMT}, date-modified = {2014-06-03T08:54:33GMT}, editor = {Dedner, Andreas and Flemisch, Bernd and Kl{\"o}fkorn, Robert}, isbn = {978-3-642-28589-9}, month = {04}, owner = {kaulmann}, publisher = {Springer}, rating = {0}, read = {Yes}, title = {{A Software Framework for Reduced Basis Methods Using DUNE-RB and RBMATLAB}}, url = {http://www.springer.com/engineering/computational+intelligence+and+complexity/book/978-3-642-28588-2}, year = 2012 }
  Link
  http://www.springer.com/engineering/computational+intelligence+and+complexity/book/978-3-642-28588-2
6. B. Haasdonk, J. Salomon, and B. Wohlmuth, “A Reduced Basis Method for the Simulation of American Options,” 2012. [Online]. Available: http://arxiv.org/pdf/1201.3289v1
  - BibTeX
  - Link
  BibTeX
  @inproceedings{Haasdonk2012, author = {Haasdonk, Bernard and Salomon, J. and Wohlmuth, B.}, booktitle = {ENUMATH 2011 Proceedings}, groups = {haasdonk, haasdonk_all_papers}, owner = {haasdonk}, title = {A Reduced Basis Method for the Simulation of {A}merican Options}, url = {http://arxiv.org/pdf/1201.3289v1}, year = 2012 }
  Link
  http://arxiv.org/pdf/1201.3289v1
7. B. Haasdonk, J. Salomon, and B. Wohlmuth, “A Reduced Basis Method for Parametrized Variational Inequalities,” SIAM Journal on Numerical Analysis, vol. 50, no. 5, Art. no. 5, 2012.
  - BibTeX
  BibTeX
  @article{Haasdonk2012a, author = {Haasdonk, Bernard and Salomon, J. and Wohlmuth, B.}, file = {:PDF/Haasdonk2012a_www_preprint_RB_variational_inequalities_before_SINUM.pdf:PDF;:PDF/Haasdonk2012a_SINUM_RB_variational_inequalities.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, journal = {SIAM Journal on Numerical Analysis}, number = 5, owner = {haasdonk}, pages = {2656--2676}, title = {A Reduced Basis Method for Parametrized Variational Inequalities}, type = {SimTech Preprint}, volume = 50, year = 2012 }
8. T. Ruiner, J. Fehr, B. Haasdonk, and P. Eberhard, “A-posteriori error estimation for second order mechanical systems,” Acta Mechanica Sinica, vol. 28(3), pp. 854--862, 2012.
  - BibTeX
  BibTeX
  @article{Ruiner2012, author = {Ruiner, T. and Fehr, J. and Haasdonk, Bernard and Eberhard, P.}, groups = {haasdonk, haasdonk_all_papers}, journal = {Acta Mechanica Sinica}, owner = {dihlmann}, pages = {854--862}, title = {A-posteriori error estimation for second order mechanical systems}, volume = {28(3)}, year = 2012 }
9. S. Waldherr and B. Haasdonk, “Efficient Parametric Analysis of the Chemical Master Equation through Model Order Reduction,” BMC Systems Biology, vol. 6, p. 81, 2012, [Online]. Available: http://www.biomedcentral.com/1752-0509/6/81
  - BibTeX
  - Link
  BibTeX
  @article{waldherr2012efficient, author = {Waldherr, S. and Haasdonk, B.}, journal = {BMC Systems Biology}, owner = {haasdonk}, pages = 81, title = {Efficient Parametric Analysis of the Chemical Master Equation through Model Order Reduction}, url = {http://www.biomedcentral.com/1752-0509/6/81}, volume = 6, year = 2012 }
  Link
  http://www.biomedcentral.com/1752-0509/6/81
10. D. Wirtz, N. Karajan, and B. Haasdonk, “Model order reduction of multiscale models using kernel methods,” SRC SimTech, University of Stuttgart, Germany, Preprint, Jun. 2012.
  - BibTeX
  BibTeX
  @techreport{wirtz2012model, author = {Wirtz, D. and Karajan, N. and Haasdonk, B.}, file = {:/home/dwirtz/aghhome/Papers/WKH13_preprint.pdf:PDF}, institution = {SRC SimTech, University of Stuttgart, Germany}, month = {06}, note = {Submitted}, owner = {dwirtz}, title = {Model order reduction of multiscale models using kernel methods}, type = {Preprint}, year = 2012 }
11. D. Wirtz and B. Haasdonk, “An Improved Vectorial Kernel Orthogonal Greedy Algorithm,” University of Stuttgart, SimTech Preprint, 2012. [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=742
  - BibTeX
  - Link
  BibTeX
  @techreport{Wirtz2012, abstract = {This work is concerned with derivation and analysis of a modifed vectorial kernel orthogonal greedy algorithm (VKOGA) for approximation of nonlinear vectorial functions. The algorithm pursues simultaneous approximation of all vector components over a shared linear subspace of the underlying function Hilbert space in a greedy fashion [14, 33] and inherits the selection principle of the f=P-Greedy algorithm [18]. For the considered algorithm we perform a limit analysis of the selection criteria for already included subspace basis functions. We show that the approximation gain is bounded globally and for the multivariate case the limit functions correspond to a directional Hermite interpolation. We further prove algebraic convergence similar to [13], improved by a dimension-dependent factor, and introduce a new a-posteriori error bound. Comparison to related variants of our algorithm are presented. Targeted applications of this algorithm are model reduction of multiscale models [40].}, author = {Wirtz, Daniel and Haasdonk, Bernard}, file = {:PDF/WH12c_preprint.pdf:PDF}, groups = {Greedy}, institution = {University of Stuttgart}, note = {{I}n preparation}, owner = {haasdonk}, title = {An Improved Vectorial Kernel Orthogonal Greedy Algorithm}, type = {SimTech Preprint}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=742}, year = 2012 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=742
12. D. Wirtz, D. C. Sorensen, and B. Haasdonk, “A-posteriori error estimation for DEIM reduced nonlinear dynamical systems,” University of Stuttgart, SimTech Preprint, Oct. 2012. [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=733
  - BibTeX
  - Link
  BibTeX
  @techreport{Wirtz2012b, abstract = {In this work an effcient approach for a-posteriori error estimation for POD-DEIM reduced nonlinear dynamical systems is introduced. The considered nonlinear systems may also include time and parameter-affne linear terms as well as parametrically dependent inputs and outputs. The reduction process involves a Galerkin projection of the full system and approximation of the system's nonlinearity by the DEIM method [Chaturantabut & Sorensen (2010)]. The proposed a-posteriori error estimator can be effciently decomposed in an offine/online fashion and is obtained by a one dimensional auxiliary ODE during reduced simulations. Key elements for effcient online computation are partial similarity transformations and matrix DEIM approximations of the nonlinearity Jacobians. The theoretical results are illustrated by application to an unsteady Burgers equation and a cell apoptosis model.}, author = {Wirtz, Daniel and Sorensen, D.C. and Haasdonk, Bernard}, file = {:PDF/WSH12_pre.pdf:PDF}, institution = {University of Stuttgart}, month = {10}, note = {Submitted to SISC}, owner = {haasdonk}, title = {A-posteriori error estimation for DEIM reduced nonlinear dynamical systems}, type = {SimTech Preprint}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=733}, year = 2012 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=733
13. D. Wirtz and B. Haasdonk, “A-posteriori error estimation for parameterized kernel-based systems,” 2012. [Online]. Available: http://www.ifac-papersonline.net/
  - BibTeX
  - Link
  BibTeX
  @inproceedings{wirtz2012aposteriori, abstract = {This work is concerned with derivation of fully offine/online decomposable effcient aposteriori error estimators for reduced parameterized nonlinear kernel-based systems. The dynamical systems under consideration consist of a nonlinear, time- and parameter-dependent kernel expansion representing the system's inner dynamics as well as time- and parameter-affne inputs, initial conditions and outputs. The estimators are established for a reduction technique originally proposed in [7] and are an extension of the estimators derived in [11] to the fully time-dependent, parameterized setting. Key features for the effcient error estimation are to use local Lipschitz constants provided by a certain class of kernels and an iterative scheme to balance computation cost against estimation sharpness. Together with the affnely time/parameter-dependent system components a full offine/online decomposition for both the reduction process and the error estimators is possible. Some experimental results for synthetic systems illustrate the effcient evaluation of the derived error estimators for different parameters.}, author = {Wirtz, Daniel and Haasdonk, Bernard}, booktitle = {Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling}, owner = {haasdonk}, title = {A-posteriori error estimation for parameterized kernel-based systems}, url = {http://www.ifac-papersonline.net/}, year = 2012 }
  Link
  http://www.ifac-papersonline.net/
14. D. Wirtz and B. Haasdonk, “Efficient a-posteriori error estimation for nonlinear kernel-based reduced systems,” Systems & Control Letters, vol. 61, no. 1, Art. no. 1, 2012, doi: 10.1016/j.sysconle.2011.10.012.
  - BibTeX
  - Link
  BibTeX
  @article{WH12, abstract = {In this paper, we consider the topic of model reduction for nonlinear dynamical systems based on kernel expansions. Our approach allows for a full offline/online decomposition and efficient online computation of the reduced model. In particular, we derive an a-posteriori state-space error estimator for the reduction error. A key ingredient is a local Lipschitz constant estimation that enables rigorous a-posteriori error estimation. The computation of the error estimator is realized by solving an auxiliary differential equation during online simulations. Estimation iterations can be performed that allow a balancing between estimation sharpness and computation time. Numerical experiments demonstrate the estimation improvement over different estimator versions and the rigor and effectiveness of the error bounds.}, author = {Wirtz, Daniel and Haasdonk, Bernard}, doi = {10.1016/j.sysconle.2011.10.012}, file = {:PDF/WH12_www_preprint_error_estimation_nonlinear_kernel_based_reduced_systems.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, journal = {Systems {\&} Control Letters}, number = 1, owner = {schmidta}, pages = {203--211}, publisher = {Elsevier {BV}}, title = {Efficient a-posteriori error estimation for nonlinear kernel-based reduced systems}, url = {http://dx.doi.org/10.1016/j.sysconle.2011.10.012}, volume = 61, year = 2012 }
  Link
  http://dx.doi.org/10.1016/j.sysconle.2011.10.012
2011
1. M. Dihlmann, M. Drohmann, and B. Haasdonk, “Model Reduction of Parametrized Evolution Problems using the Reduced basis Method with Adaptive Time-Partitioning,” 2011.
  - BibTeX
  BibTeX
  @inproceedings{DDH11, author = {Dihlmann, M. and Drohmann, M. and Haasdonk, Bernard}, booktitle = {Proc. of ADMOS 2011}, file = {:PDF/DDH11_www_preprint_Tpart_ADMOS2011.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, owner = {haasdonk}, title = {Model Reduction of Parametrized Evolution Problems using the Reduced basis Method with Adaptive Time-Partitioning}, year = 2011 }
2. M. Drohmann, B. Haasdonk, and M. Ohlberger, “Adaptive Reduced Basis Methods for Nonlinear Convection-Diffusion Equations,” 2011.
  - BibTeX
  BibTeX
  @inproceedings{DHO11, author = {Drohmann, M. and Haasdonk, Bernard and Ohlberger, M.}, booktitle = {In Proc. FVCA6}, file = {:PDF/UNSORTED/DHO11_FVCA_proceedings.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, owner = {dihlmann}, title = {Adaptive Reduced Basis Methods for Nonlinear Convection-Diffusion Equations}, year = 2011 }
3. B. Haasdonk, M. Dihlmann, and M. Ohlberger, “A Training Set and Multiple Basis Generation Approach for Parametrized Model Reduction Based on Adaptive Grids in Parameter Space,” Mathematical and Computer Modelling of Dynamical Systems, vol. 17, pp. 423--442, 2011.
  - BibTeX
  BibTeX
  @article{HDO11, author = {Haasdonk, Bernard and Dihlmann, M. and Ohlberger, M.}, file = {:PDF/Reduced Basis/HDO11.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, journal = {Mathematical and Computer Modelling of Dynamical Systems}, owner = {schmidta}, pages = {423--442}, title = {A Training Set and Multiple Basis Generation Approach for Parametrized Model Reduction Based on Adaptive Grids in Parameter Space}, volume = 17, year = 2011 }
4. B. Haasdonk, “Reduzierte-Basis-Methoden, Vorlesungsskript SS 2011,” University of Stuttgart, IANS-Report 2011–004, 2011.
  - BibTeX
  BibTeX
  @techreport{Haasdonk2011c, author = {Haasdonk, Bernard}, file = {:PDF/Haasdonk2011c_www_rb_lecture_script_IANS_report_0411.pdf:PDF}, groups = {haasdonk_misc, haasdonk_all_papers}, institution = {University of Stuttgart}, number = {2011-004}, owner = {haasdonk}, title = {Reduzierte-{B}asis-{M}ethoden, {V}orlesungsskript {SS} 2011}, type = {IANS-Report}, year = 2011 }
5. B. Haasdonk and B. Lohmann, “Special Issue on ‘“Model Order Reduction of Parametrized Problems,”’” Mathematical and Computer Modelling of Dynamical Systems, vol. 17, no. 4, Art. no. 4, 2011, doi: 10.1080/13873954.2011.547661.
  - BibTeX
  - Link
  BibTeX
  @article{Haasdonk2011a, author = {Haasdonk, Bernard and Lohmann, B.}, doi = {10.1080/13873954.2011.547661}, groups = {haasdonk, haasdonk_all_papers}, journal = {Mathematical and Computer Modelling of Dynamical Systems}, number = 4, owner = {haasdonk}, pages = {295--296}, title = {Special Issue on ''Model Order Reduction of Parametrized Problems''}, url = {http://www.tandfonline.com/doi/pdf/10.1080/13873954.2011.547661}, volume = 17, year = 2011 }
  Link
  http://www.tandfonline.com/doi/pdf/10.1080/13873954.2011.547661
6. B. Haasdonk and M. Ohlberger, “Efficient reduced models and a posteriori error estimation for parametrized dynamical systems by offline/online decomposition,” Math. Comput. Model. Dyn. Syst., vol. 17, no. 2, Art. no. 2, 2011, doi: 10.1080/13873954.2010.514703.
  - BibTeX
  - Link
  BibTeX
  @article{haasdonk2011efficient, author = {Haasdonk, Bernard and Ohlberger, Mario}, doi = {10.1080/13873954.2010.514703}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Haasdonk2011b_www_rb_dyn_sys_preprint.pdf:PDF}, fjournal = {Mathematical and Computer Modelling of Dynamical Systems. Methods, Tools and Applications in Engineering and Related Sciences}, issn = {1387-3954}, journal = {Math. Comput. Model. Dyn. Syst.}, mrclass = {65L05 (93B11)}, mrnumber = {2784465 (2012d:65126)}, mrreviewer = {M. Krastanov}, number = 2, owner = {haasdonk}, pages = {145--161}, title = {Efficient reduced models and {\it a posteriori} error estimation for parametrized dynamical systems by offline/online decomposition}, url = {http://dx.doi.org/10.1080/13873954.2010.514703}, volume = 17, year = 2011 }
  Link
  http://dx.doi.org/10.1080/13873954.2010.514703
7. N. Jung, A. T. Patera, B. Haasdonk, and B. Lohmann, “Model Order Reduction and Error Estimation with an Application to the Parameter-Dependent Eddy Current Equation,” Mathematical and Computer Modelling of Dynamical Systems, vol. 17, no. 4, Art. no. 4, 2011, doi: 10.1080/13873954.2011.582120.
  - BibTeX
  - Link
  BibTeX
  @article{Jung2011, author = {Jung, N. and Patera, A.T. and Haasdonk, Bernard and Lohmann, B.}, doi = {10.1080/13873954.2011.582120}, groups = {haasdonk, haasdonk_all_papers}, journal = {Mathematical and Computer Modelling of Dynamical Systems}, number = 4, owner = {dwirtz}, pages = {561--582}, title = {Model Order Reduction and Error Estimation with an Application to the Parameter-Dependent Eddy Current Equation}, url = {http://www.tandfonline.com/doi/abs/10.1080/13873954.2011.582120}, volume = 17, year = 2011 }
  Link
  http://www.tandfonline.com/doi/abs/10.1080/13873954.2011.582120
8. S. Kaulmann, M. Ohlberger, and B. Haasdonk, “A new local reduced basis discontinuous Galerkin approach for heterogeneous multiscale problems,” Comptes Rendus Mathematique, vol. 349, no. 23–24, Art. no. 23–24, Dec. 2011, doi: 10.1016/j.crma.2011.10.024.
  - BibTeX
  - Link
  BibTeX
  @article{kaulmann2011local, abstract = {Inspired by the reduced basis approach and modern numerical multiscale methods, we present a new framework for an efficient treatment of heterogeneous multiscale problems. The new approach is based on the idea of considering heterogeneous multiscale problems as parametrized partial differential equations where the parameters are smooth functions. We then construct, in an offline phase, a suitable localized reduced basis that is used in an online phase to efficiently compute approximations of the multiscale problem by means of a discontinuous Galerkin method on a coarse grid. We present our approach for elliptic multiscale problems and discuss an a posteriori error estimate that can be used in the construction process of the localized reduced basis. Numerical experiments are given to demonstrate the efficiency of the new approach.}, author = {Kaulmann, Sven and Ohlberger, Mario and Haasdonk, Bernard}, date-added = {2012-10-24T14:53:21GMT}, date-modified = {2014-01-29T11:58:01GMT}, doi = {10.1016/j.crma.2011.10.024}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Kaulmann2011_www_CRAS_New_Local_RBDG.pdf:PDF}, journal = {Comptes Rendus Mathematique}, month = {12}, number = {23-24}, owner = {kaulmann}, pages = {1233--1238}, rating = {0}, read = {Yes}, title = {{A new local reduced basis discontinuous Galerkin approach for heterogeneous multiscale problems}}, url = {http://www.sciencedirect.com/science/article/pii/S1631073X11003074}, volume = 349, year = 2011 }
  Link
  http://www.sciencedirect.com/science/article/pii/S1631073X11003074
2010
1. M. Drohmann, B. Haasdonk, and M. Ohlberger, “Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation,” University of Münster, Preprint Angewandte Mathematik und Informatik 02/10-N, 2010.
  - BibTeX
  BibTeX
  @techreport{DHO10, author = {Drohmann, M. and Haasdonk, Bernard and Ohlberger, M.}, file = {:PDF/DHO10_www_preprint_muenster.pdf:PDF}, institution = {University of M\"unster}, note = {Submitted to SISC}, number = {02/10-N}, owner = {haasdonk}, title = {Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation}, type = {Preprint Angewandte Mathematik und Informatik}, year = 2010 }
2. B. Haasdonk, “Effiziente und Gesicherte Modellreduktion für Parametrisierte Dynamische Systeme.,” at - Automatisierungstechnik, vol. 58, no. 8, Art. no. 8, 2010.
  - BibTeX
  BibTeX
  @article{Ha10, author = {Haasdonk, Bernard}, file = {:PDF/Ha10_automatisierungstechnik_effiziente_gesicherte_RB.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, journal = {at - Automatisierungstechnik}, number = 8, owner = {haasdonk}, pages = {468--474}, title = {Effiziente und Gesicherte {M}odellreduktion f{\"u}r Parametrisierte Dynamische {S}ysteme.}, volume = 58, year = 2010 }
3. B. Haasdonk, M. Dihlmann, and M. Ohlberger, “A Training Set and Multiple Bases Generation Approach for Parametrized Model Reduction Based on Adaptive Grids in Parameter Space.,” University of Stuttgart, 2010.
  - BibTeX
  BibTeX
  @techreport{HDO10, author = {Haasdonk, Bernard and Dihlmann, M. and Ohlberger, M.}, file = {:PDF/HDO10_www_preprint_training_set_multiple_basis_RB.pdf:PDF}, institution = {University of Stuttgart}, note = {Submitted to MCMDS}, owner = {haasdonk}, title = {A Training Set and Multiple Bases Generation Approach for Parametrized Model Reduction Based on Adaptive Grids in Parameter Space.}, year = 2010 }
4. E. Pekalska and B. Haasdonk, “Indefinite Kernel Discriminant Analysis,” 2010.
  - BibTeX
  BibTeX
  @inproceedings{Pekalska2010, author = {Pekalska, E. and Haasdonk, Bernard}, booktitle = {Proc. COMPSTAT 2010, International Conference on Computational Statistics}, file = {:PDF/Pekalska2010_www_COMPSTAT2010.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, owner = {haasdonk}, title = {Indefinite Kernel Discriminant Analysis}, year = 2010 }
2009
1. M. Drohmann, B. Haasdonk, and M. Ohlberger, “Reduced Basis Method for Finite Volume Approximation of Evolution Equations on Parametrized Geometries,” 2009.
  - BibTeX
  BibTeX
  @unpublished{DHO08preprint, author = {Drohmann, M. and Haasdonk, Bernard and Ohlberger, M.}, file = {:PDF/Reduced Basis/DHO08preprint.pdf:PDF}, owner = {santinge}, title = {Reduced Basis Method for Finite Volume Approximation of Evolution Equations on Parametrized Geometries}, year = 2009 }
2. B. Haasdonk, M. Ohlberger, T. Tonn, and K. Urban, MoRePaS 2009 Book of Abstracts. University of Münster, 2009.
  - BibTeX
  BibTeX
  @book{haasdonk2009morepas, author = {Haasdonk, B. and Ohlberger, M. and Tonn, T. and Urban, K.}, owner = {haasdonk}, publisher = {University of Münster}, title = {MoRePaS 2009 Book of Abstracts}, year = 2009 }
3. B. Haasdonk and M. Ohlberger, “Efficient a-posteriori Error Estimation for Parametrized Reduced Dynamical Systems,” 2009.
  - BibTeX
  BibTeX
  @inproceedings{haasdonk2009efficient, author = {Haasdonk, B. and Ohlberger, M.}, booktitle = {GMA-Fachaussschuss 1.30, Tagungsband}, owner = {haasdonk}, title = {Efficient a-posteriori Error Estimation for Parametrized Reduced Dynamical Systems}, year = 2009 }
4. B. Haasdonk and M. Ohlberger, “Space-Adaptive Reduced Basis Simulation for Time-Dependent Problems,” 2009. [Online]. Available: http://www.ians.uni-stuttgart.de/am/Haasdonk/publications/mathmod2009_Nadapt.pdf
  - BibTeX
  - Link
  BibTeX
  @inproceedings{HO09a, author = {Haasdonk, Bernard and Ohlberger, M.}, booktitle = {Proc. MATHMOD 2009, 6th Vienna International Conference on Mathematical Modelling}, file = {:PDF/HO09a_Mathmod2009_space_adaptive_RB.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, owner = {haasdonk}, title = {Space-Adaptive Reduced Basis Simulation for Time-Dependent Problems}, url = {http://www.ians.uni-stuttgart.de/am/Haasdonk/publications/mathmod2009_Nadapt.pdf}, year = 2009 }
  Link
  http://www.ians.uni-stuttgart.de/am/Haasdonk/publications/mathmod2009_Nadapt.pdf
5. B. Haasdonk and M. Ohlberger, “Efficient Reduced Models for Parametrized Dynamical Systems by Offline/Online Decomposition,” 2009. [Online]. Available: http://www.ians.uni-stuttgart.de/am/Haasdonk/publications/mathmod2009_PMOR.pdf
  - BibTeX
  - Link
  BibTeX
  @inproceedings{HO09, author = {Haasdonk, Bernard and Ohlberger, M.}, booktitle = {Proc. MATHMOD 2009, 6th Vienna International Conference on Mathematical Modelling}, file = {:PDF/HO09_Mathmod2009_efficient_reduced_models_dyn_sys.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, owner = {haasdonk}, title = {Efficient Reduced Models for Parametrized Dynamical Systems by Offline/Online Decomposition}, url = {http://www.ians.uni-stuttgart.de/am/Haasdonk/publications/mathmod2009_PMOR.pdf}, year = 2009 }
  Link
  http://www.ians.uni-stuttgart.de/am/Haasdonk/publications/mathmod2009_PMOR.pdf
6. B. Haasdonk and M. Ohlberger, “Reduced basis method for explicit finite volume approximations of nonlinear conservation laws,” in Hyperbolic problems: theory, numerics and applications, vol. 67, Providence, RI: Amer. Math. Soc., 2009, pp. 605--614.
  - BibTeX
  BibTeX
  @incollection{Haasdonk2009, address = {Providence, RI}, author = {Haasdonk, Bernard and Ohlberger, M.}, booktitle = {Hyperbolic problems: theory, numerics and applications}, file = {:PDF/Haasdonk2009_hyp2008_RB_for_nonlinear_conservation_laws.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, mrclass = {65M08 (35L65 76M12)}, mrnumber = {MR2605256}, owner = {haasdonk}, pages = {605--614}, publisher = {Amer. Math. Soc.}, series = {Proc. Sympos. Appl. Math.}, title = {Reduced basis method for explicit finite volume approximations of nonlinear conservation laws}, volume = 67, year = 2009 }
7. N. Jung, B. Haasdonk, and D. Kröner, “Reduced Basis Method for Quadratically Nonlinear Transport Equations,” University of Stuttgart, Preprint SimTech 2009–15, 2009.
  - BibTeX
  BibTeX
  @techreport{JHK09, author = {Jung, N. and Haasdonk, Bernard and Kr{\"o}ner, D.}, institution = {University of Stuttgart}, journal = {IJCSM}, note = {Accepted by IJCSM}, number = {2009-15,}, owner = {haasdonk}, title = {Reduced Basis Method for Quadratically Nonlinear Transport Equations}, type = {Preprint SimTech}, year = 2009 }
8. E. Pekalska and B. Haasdonk, “Kernel Discriminant Analysis with Positive Definite and Indefinite Kernels,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 31, no. 6, Art. no. 6, 2009.
  - BibTeX
  BibTeX
  @article{Pekalska2009, author = {Pekalska, E. and Haasdonk, Bernard}, groups = {haasdonk, haasdonk_all_papers}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, number = 6, owner = {haasdonk}, pages = {1017-1032}, title = {Kernel Discriminant Analysis with Positive Definite and Indefinite Kernels}, volume = 31, year = 2009 }
2008
1. M. Drohmann, B. Haasdonk, and M. Ohlberger, “Reduced Basis Method for Finite Volume Approximation of Evolution Equations on Parametrized Geometries,” in Proceedings of ALGORITMY 2009, 2008, pp. 111--120. [Online]. Available: http://pc2.iam.fmph.uniba.sk/amuc/_contributed/algo2009/drohmann.pdf
  - BibTeX
  - Link
  BibTeX
  @inproceedings{DHO08, author = {Drohmann, M. and Haasdonk, Bernard and Ohlberger, M.}, booktitle = {Proceedings of ALGORITMY 2009}, file = {:PDF/DHO08_www_algorithmy_geometry_parameters_RB.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, owner = {m_droh01}, pages = {111--120}, title = {Reduced Basis Method for Finite Volume Approximation of Evolution Equations on Parametrized Geometries}, url = {http://pc2.iam.fmph.uniba.sk/amuc/_contributed/algo2009/drohmann.pdf}, year = 2008 }
  Link
  http://pc2.iam.fmph.uniba.sk/amuc/_contributed/algo2009/drohmann.pdf
2. B. Haasdonk and M. Ohlberger, “Adaptive basis enrichment for the reduced basis method applied to finite volume schemes,” in Finite volumes for complex applications V, ISTE, London, 2008, pp. 471--478.
  - BibTeX
  BibTeX
  @incollection{haasdonk2008adaptive, author = {Haasdonk, B. and Ohlberger, M.}, booktitle = {Finite volumes for complex applications {V}}, mrclass = {65M06}, mrnumber = {MR2451442}, owner = {haasdonk}, pages = {471--478}, publisher = {ISTE, London}, title = {Adaptive basis enrichment for the reduced basis method applied to finite volume schemes}, year = 2008 }
3. B. Haasdonk and E. Pekalska, “Indefinite Kernel Fisher Discriminant,” 2008.
  - BibTeX
  BibTeX
  @inproceedings{haasdonk2008indefinite, author = {Haasdonk, B. and Pekalska, E.}, booktitle = {Proc. ICPR 2008, International Conference on Pattern Recognition}, note = {(C) IEEE 2008}, owner = {haasdonk}, title = {Indefinite Kernel {F}isher Discriminant}, year = 2008 }
4. B. Haasdonk and M. Ohlberger, “Reduced basis method for finite volume approximations of parametrized linear evolution equations,” ESAIM: M2AN, vol. 42, no. 2, Art. no. 2, Mar. 2008, doi: 10.1051/m2an:2008001.
  - BibTeX
  - Link
  BibTeX
  @article{HO08, author = {Haasdonk, Bernard and Ohlberger, M.}, doi = {10.1051/m2an:2008001}, file = {:PDF/Reduced Basis/HO08_Reduced basis method for finite volume approximations of parametrized linear evolution equations_journal.pdf:PDF}, groups = {Reduced Basis, Parabolic, haasdonk, haasdonk_all_papers}, journal = {ESAIM: M2AN}, month = {03}, number = 2, pages = {277--302}, title = {Reduced basis method for finite volume approximations of parametrized linear evolution equations}, url = {http://dx.doi.org/10.1051/m2an:2008001}, volume = 42, year = 2008 }
  Link
  http://dx.doi.org/10.1051/m2an:2008001
5. B. Haasdonk and E. Pekalska, “Classification with Kernel Mahalanobis Distances,” 2008.
  - BibTeX
  BibTeX
  @inproceedings{Haasdonk2008d, author = {Haasdonk, Bernard and Pekalska, E.}, booktitle = {Proc. of 32nd. GfKl Conference, Advances in Data Analysis, Data Handling and Business Intelligence}, file = {:PDF/Haasdonk2008d_Gfkl2008_kernel_mahalanobis_distances.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, owner = {haasdonk}, title = {Classification with Kernel {M}ahalanobis Distances}, year = 2008 }
6. B. Haasdonk, M. Ohlberger, and G. Rozza, “A Reduced Basis Method for Evolution Schemes with Parameter-Dependent Explicit Operators,” ETNA, Electronic Transactions on Numerical Analysis, vol. 32, pp. 145--161, 2008, [Online]. Available: http://etna.mcs.kent.edu/vol.32.2008/pp145-161.dir/pp145-161.pdf
  - BibTeX
  - Link
  BibTeX
  @article{HOR08, author = {Haasdonk, Bernard and Ohlberger, M. and Rozza, G.}, file = {:PDF/HOR08_www_preprint_EOI_explicit_operators_before_ETNA.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, journal = {ETNA, Electronic Transactions on Numerical Analysis}, owner = {bhaas_01}, pages = {145--161}, title = {A Reduced Basis Method for Evolution Schemes with Parameter-Dependent Explicit Operators}, url = {http://etna.mcs.kent.edu/vol.32.2008/pp145-161.dir/pp145-161.pdf}, volume = 32, year = 2008 }
  Link
  http://etna.mcs.kent.edu/vol.32.2008/pp145-161.dir/pp145-161.pdf
7. E. Pekalska and B. Haasdonk, “Kernel Quadratic Discriminant Analysis with Positive and Indefinite Kernels,” University of Münster, Preprint Angewandte Mathematik und Informatik 06/08, 2008.
  - BibTeX
  BibTeX
  @techreport{Pekalska2008a, author = {Pekalska, E. and Haasdonk, Bernard}, file = {:PDF/Pekalska2008a_www_preprint_Kernel_Quad_Discr_Analysis_Positive_Indefinite_Kernels.pdf:PDF}, groups = {haasdonk_misc, haasdonk_all_papers}, institution = {University of M{\"u}nster}, number = {06/08}, owner = {haasdonk}, title = {Kernel Quadratic Discriminant Analysis with Positive and Indefinite Kernels}, type = {Preprint Angewandte Mathematik und Informatik}, year = 2008 }
2007
1. J. Fuhrmann, B. Haasdonk, E. Holzbecher, and M. Ohlberger, “Guest Editorial for Special Issue on Modelling and Simulation of PEM-FC,” Journal of Fuel Cell Science and Technology, 2007.
  - BibTeX
  BibTeX
  @article{FHHO07, author = {Fuhrmann, J. and Haasdonk, Bernard and Holzbecher, E. and Ohlberger, M.}, groups = {haasdonk, haasdonk_all_papers}, journal = {Journal of Fuel Cell Science and Technology}, owner = {haasdonk}, title = {Guest Editorial for Special Issue on Modelling and Simulation of {PEM-FC}}, year = 2007 }
2. B. Haasdonk and M. Ohlberger, “Basis Construction for Reduced Basis Methods By Adaptive Parameter Grids,” in Proc. International Conference on Adaptive Modeling and Simulation, ADMOS 2007, 2007.
  - BibTeX
  BibTeX
  @inproceedings{haasdonk2007basis, abstract = {An important step in parametrized PDE-based model reduction with reduced basis methods is the generation of a reduced basis space, on which the detailed numerical simula- tions are projected. We present a new strategy for this reduced basis generation. We apply an effective exploration of the parameter space by adaptive grids. The resulting method gives a considerable improvement concerning equal distribution of the model error over the parameter space compared to ?xed or uniformly re?ned grids. It is computationally very effective in terms of small ratio of training-time and model-error.}, author = {Haasdonk, B. and Ohlberger, M.}, booktitle = {Proc. International Conference on Adaptive Modeling and Simulation, ADMOS 2007}, editor = {D\'iez, P. and Runesson, K.}, owner = {haasdonk}, publisher = {CIMNE, Barcelona}, title = {Basis Construction for Reduced Basis Methods By Adaptive Parameter Grids}, year = 2007 }
3. B. Haasdonk, M. Ohlberger, and G. Rozza, “A Reduced Basis Method for Evolution Schemes with Parameter-Dependent Explicit Operators,” University of Münster, 09/07-N, FB 10, 2007.
  - BibTeX
  BibTeX
  @techreport{HOR07, abstract = {During the last decades, reduced basis (RB) methods have been developed to a wide methodology for model reduction of problems that are governed by parametrized partial differential equations ($P^2DE$s ). In particular equations of elliptic and parabolic type for linear, low polynomial or monotonic nonlinearities have been treated successfully by RB methods using ï¬nite element schemes. Due to the characteristic ofï¬‚ine-online decomposition, the reduced models often become suitable for a multi-query or real-time setting, where simulation results, such as ï¬eld-variables or output estimates, can be approximated reliably and rapidly for varying parameters. In the current study, we address a certain class of time-dependent evolution schemes with explicit discretization operators that are arbitrarily parameter dependent. We extend the RB-methodology to these cases by applying the empirical interpolation method to localized discretization operators. The main technical ingredients are: (i) generation of a collateral reduced basis modelling the effects of the discretization operator under parameter variations in the ofï¬‚ine-phase and (ii) an online simulation scheme based on a numerical subgrid and localized evaluations of the evolution operator. We formulate an a-posteriori error estimator for quantiï¬cation of the resulting reduced simulation error. Numerical experiments on a parametrized convection problem, discretized with a ï¬nite volume scheme, demonstrate the applicability of the model reduction technique. We obtain a parametrized reduced model, which enables parameter variation with fast simulation response. We quantify the computational gain with respect to the non-reduced model and investigate the error convergence.}, author = {Haasdonk, Bernard and Ohlberger, M. and Rozza, G.}, file = {:PDF/HOR07_www_preprint_EOI_explicit_operators_before_ETNA.pdf:PDF}, groups = {haasdonk_misc, haasdonk_all_papers}, institution = {University of M{\"u}nster}, note = {Accepted by ETNA.}, number = {09/07 - N, FB 10}, owner = {haasdonk}, title = {A Reduced Basis Method for Evolution Schemes with Parameter-Dependent Explicit Operators}, year = 2007 }
4. B. Haasdonk and H. Burkhardt, “Invariant Kernels for Pattern Analysis and Machine Learning,” Machine Learning, vol. 68, pp. 35--61, 2007, doi: DOI 10.1007/s10994-007-5009-7.
  - BibTeX
  BibTeX
  @article{Haasdonk2007, author = {Haasdonk, Bernard and Burkhardt, H.}, doi = {DOI 10.1007/s10994-007-5009-7}, file = {:PDF/Haasdonk2007_machine_learning_invariant_kernels.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, institution = {IIF-LMB, Universit{\"a}t Freiburg, Institut f{\"u}r Informatik}, journal = {Machine Learning}, owner = {haasdonk}, pages = {35--61}, title = {Invariant Kernels for Pattern Analysis and Machine Learning}, volume = 68, year = 2007 }
5. B. Haasdonk and H. Burkhardt, “Classification with Invariant Distance Substitution Kernels,” 2007.
  - BibTeX
  BibTeX
  @inproceedings{Haasdonk2007b, author = {Haasdonk, Bernard and Burkhardt, H.}, booktitle = {Proc. of 31st GfKl Conference, Data Analysis, Machine Learning, and Applications}, file = {:PDF/Haasdonk2007b_www_classification_invariant_kernels_GfKl2007.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, owner = {haasdonk}, title = {Classification with Invariant Distance Substitution Kernels}, year = 2007 }
2006
1. B. Haasdonk and M. Ohlberger, “Reduced Basis Method for Finite Volume Approximations of Parametrized Evolution Equations,” University of Freiburg, Institute of Applied Mathematics, 12/2006, 2006.
  - BibTeX
  BibTeX
  @techreport{Haasdonk2006a, author = {Haasdonk, Bernard and Ohlberger, M.}, file = {:PDF/Haasdonk2006b_www_RB_lin_FV_preprint_before_M2AN.pdf:PDF}, groups = {haasdonk_misc, haasdonk_all_papers}, institution = {University of Freiburg, Institute of Applied Mathematics}, note = {Extended version of M2AN article.}, number = {12/2006}, owner = {haasdonk}, title = {Reduced Basis Method for Finite Volume Approximations of Parametrized Evolution Equations}, year = 2006 }
2. B. Haasdonk, R. Klöfkorn, M. Ohlberger, J. Schumacher, and K. Steinkamp, “Complete 3D-Modelling of a PEM Fuel Cell and Stack,” Universität Freiburg, Abteilung für Angewandte Mathematik, 2006.
  - BibTeX
  BibTeX
  @techreport{Haasdonk2006, author = {Haasdonk, Bernard and Kl{\"o}fkorn, R. and Ohlberger, M. and Schumacher, J. and Steinkamp, K.}, file = {:PDF/Haasdonk2006b.pdf:PDF}, institution = {Universit{\"a}t Freiburg, Abteilung f{\"u}r Angewandte Mathematik}, note = {In Vorbereitung}, owner = {haasdonk}, title = {Complete 3D-Modelling of a PEM Fuel Cell and Stack}, year = 2006 }
3. K.-D. Peschke et al., “Using Transformation Knowledge for the Classification of Raman Spectra of Biological Samples,” in BIOMED 2006, Proc. of the 4th IASTED International Conference on Biomedical Engineering, 2006, pp. 288–293.
  - BibTeX
  BibTeX
  @inproceedings{peschke2006using, author = {Peschke, K.-D. and Haasdonk, B. and Ronneberger, O. and Burkhard, H. and R\"osch, P. and Harz, M. and Popp, J.}, booktitle = {BIOMED 2006, Proc. of the 4th IASTED International Conference on Biomedical Engineering}, owner = {haasdonk}, pages = {288-293}, title = {Using Transformation Knowledge for the Classification of {R}aman Spectra of Biological Samples}, year = 2006 }
2005
1. B. Haasdonk, A. Vossen, and H. Burkhardt, “Invariance in Kernel Methods by Haar-Integration Kernels,” 2005.
  - BibTeX
  BibTeX
  @inproceedings{haasdonk2005invariance, author = {Haasdonk, B. and Vossen, A. and Burkhardt, H.}, booktitle = {Proceedings of the 14th Scandinavian Conference on Image Analysis}, owner = {haasdonk}, publisher = {Springer}, title = {Invariance in Kernel Methods by {H}aar-Integration Kernels}, year = 2005 }
2. B. Haasdonk and H. Burkhardt, “Invariant Kernels for Pattern Analysis and Machine Learning,” IIF-LMB, Universität Freiburg, Institut für Informatik, 3/05, Aug. 2005.
  - BibTeX
  BibTeX
  @techreport{Haasdonk2005, author = {Haasdonk, Bernard and Burkhardt, H.}, institution = {IIF-LMB, Universit{\"a}t Freiburg, Institut f{\"u}r Informatik}, month = {08}, number = {3/05}, owner = {haasdonk}, title = {Invariant Kernels for Pattern Analysis and Machine Learning}, year = 2005 }
3. B. Haasdonk, “Transformation Knowledge in Pattern Analysis with Kernel Methods, Distance and Integration Kernels,” Albert-Ludwigs-Universität, Freiburg im Breisgau, Fakultät für Angewandte Wissenschaften, 2005.
  - BibTeX
  BibTeX
  @phdthesis{Ha05, author = {Haasdonk, Bernard}, file = {:PDF/Ha05_www_Dissertation_Uni_Freiburg.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, month = {Mai}, note = {Published 2006 as ISBN-3-8322-5026-3, Shaker-Verlag, Aachen, and Online at http://www.freidok.uni-freiburg.de/volltexte/2376}, owner = {habiger-sebastian}, school = {Albert-Ludwigs-Universit{\"a}t, Freiburg im Breisgau, Fakult{\"a}t f{\"u}r Angewandte Wissenschaften}, title = {Transformation Knowledge in Pattern Analysis with Kernel Methods, Distance and Integration Kernels}, year = 2005 }
4. B. Haasdonk, “Feature Space Interpretation of SVMs with Indefinite Kernels,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 4, Art. no. 4, 2005, doi: http://doi.ieeecomputersociety.org/10.1109/TPAMI.2005.78.
  - BibTeX
  BibTeX
  @article{H05, address = {Los Alamitos, CA, USA}, author = {Haasdonk, Bernard}, doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2005.78}, file = {:PDF/H05_IEEE_TPAMI_feature_space_indefinite_SVM.pdf:PDF;:PDF/H05_IEEE_TPAMI_feature_space_indefinite_SVM_appendix.pdf:PDF;}, groups = {haasdonk, haasdonk_all_papers}, issn = {0162-8828}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, number = 4, pages = {482-492}, publisher = {IEEE Computer Society}, title = {Feature Space Interpretation of {SVMs} with Indefinite Kernels}, volume = 27, year = 2005 }
2004
1. B. Haasdonk and C. Bahlmann, “Learning with Distance Substitution Kernels,” in Pattern Recognition - Proceedings of the 26th DAGM Symposium, 2004, pp. 220–227.
  - BibTeX
  BibTeX
  @inproceedings{haasdonk2004learning, author = {Haasdonk, B. and Bahlmann, C.}, booktitle = { Pattern Recognition - Proceedings of the 26th {DAGM} Symposium}, owner = {haasdonk}, pages = {220-227}, publisher = {Springer}, title = {Learning with Distance Substitution Kernels}, year = 2004 }
2. B. Haasdonk, A. Halawani, and H. Burkhardt, “Adjustable invariant features by partial Haar-integration,” in Proceedings of the 17th International Conference on Pattern Recognition, 2004, vol. 2, no. 2, pp. 769–774. doi: http://dx.doi.org/10.1109/ICPR.2004.1334372.
  - BibTeX
  BibTeX
  @inproceedings{HHB04, author = {Haasdonk, Bernard and Halawani, A. and Burkhardt, H.}, booktitle = {Proceedings of the 17th International Conference on Pattern Recognition}, doi = {http://dx.doi.org/10.1109/ICPR.2004.1334372}, file = {:PDF/HHB04_partial_invariant_kernels.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, number = 2, pages = {769- 774}, title = {Adjustable invariant features by partial {H}aar-integration}, volume = 2, year = 2004 }
2003
1. H. Burkhardt and B. Haasdonk, “Mustererkennung WS 02/03, ein multimedialer Grundlagenkurs im Hauptstudium Informatik.” 2003.
  - BibTeX
  BibTeX
  @misc{burkhardt2003mustererkennung, author = {Burkhardt, H. and Haasdonk, B.}, howpublished = {CD volume, Computer Science Department, University of Freiburg}, owner = {haasdonk}, title = {Mustererkennung {WS} 02/03, ein multimedialer {G}rundlagenkurs im {H}auptstudium {I}nformatik}, year = 2003 }
2. B. Haasdonk, B. R. Poluru, and A. Teynor, “Presto-Box 1.1 Library Documentation,” IIF-LMB, Universität Freiburg, 2/03, Nov. 2003.
  - BibTeX
  BibTeX
  @techreport{Haasdonk2003, author = {Haasdonk, Bernard and Poluru, B.R. and Teynor, A.}, file = {:PDF/Haasdonk2003_www_prestobox_documentation_techrep_uni_freiburg.pdf:PDF}, groups = {haasdonk_misc, haasdonk_all_papers}, institution = {IIF-LMB, Universit{\"a}t Freiburg}, month = {11}, number = {2/03}, owner = {haasdonk}, title = {{P}resto-{B}ox 1.1 Library Documentation}, year = 2003 }
3. B. Haasdonk, M. Ohlberger, M. Rumpf, A. Schmidt, and K. G. Siebert, “Multiresolution Visualization of Higher Order Adaptive Finite Element Simulations,” Computing, vol. 70, pp. 181–204, 2003.
  - BibTeX
  BibTeX
  @article{Haasdonk2003a, author = {Haasdonk, Bernard and Ohlberger, M. and Rumpf, M. and Schmidt, A. and Siebert, K.G.}, file = {:PDF/Haasdonk2003a_multires_computing_2003.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, journal = {Computing}, owner = {haasdonk}, pages = {181-204}, title = {Multiresolution Visualization of Higher Order Adaptive Finite Element Simulations}, volume = 70, year = 2003 }
2002
1. C. Bahlmann, B. Haasdonk, and H. Burkhardt, “On-line Handwriting Recognition with Support Vector Machines - A Kernel Approach,” in Proc. of the 8th International Workshop on Frontiers in Handwriting Recognition, 2002, pp. 49--54.
  - BibTeX
  BibTeX
  @inproceedings{Bahlmann2002, abstract = {In this contribution we describe a novel classification approach for on-line handwriting recognition. The technique combines dynamic time warping (DTW) and support vector machines (SVMs) by establishing a new SVM kernel. We call this kernel \emph{Gaussian DTW (GDTW) kernel}. This kernel approach has a main advantage over common HMM techniques. It does not assume a model for the generative class conditional densities. Instead, it directly addresses the problem of discrimination by creating class boundaries and thus is less sensitive to modeling assumptions. By incorporating DTW in the kernel function, general classification problems with variable-sized sequential data can be handled. In this respect the proposed method can be straightforwardly applied to all classification problems, where DTW gives a reasonable distance measure, e.g.~speech recognition or genome processing. We show experiments with this kernel approach on the UNIPEN handwriting data, achieving results comparable to an HMM-based technique.}, author = {Bahlmann, C. and Haasdonk, Bernard and Burkhardt, H.}, booktitle = {Proc. of the 8th International Workshop on Frontiers in Handwriting Recognition}, file = {:PDF/Bahlmann2002_www_IWFHR2002.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, html = {\htmladdnormallink{{\sl Get the pdf file here}} {ftp://ftp.informatik.uni-freiburg.de/papers/lmb/ba_ha_bu_iwfhr02.pdf}}, owner = {haasdonk}, pages = {49--54}, publisher = {IEEE Computer Society}, title = {{On-line Handwriting Recognition with Support Vector Machines - A Kernel Approach}}, year = 2002 }
2. B. Haasdonk and D. Keysers, “Tangent Distance Kernels for Support Vector Machines,” in Proceedings of the 16th International Conference on Pattern Recognition, 2002, vol. 2, pp. 864–868.
  - BibTeX
  BibTeX
  @inproceedings{Haasdonk2002, abstract = {When dealing with pattern recognition problems one encounters different types of a-priori knowledge. It is important to incorporate such knowledge into the classification method at hand. A very common type of a-priori knowledge is transformation invariance of the input data, e.g.\ geometric transformations of image-data like shifts, scaling etc. Distance based classification methods can make use of this by a modified distance measure called tangent distance [13, 14]. We introduce a new class of kernels for support vector machines which incorporate tangent distance and therefore are applicable in cases where such transformation invariances are known. We report experimental results which show that the performance of our method is comparable to other state-of-the-art methods, while problems of existing ones are avoided.}, author = {Haasdonk, Bernard and Keysers, D.}, booktitle = {Proceedings of the 16th International Conference on Pattern Recognition}, file = {:PDF/Haasdonk2002_ICPR2002_tangent_distance_kernels.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, html = {\htmladdnormallink{{\sl Get the PDF file here}} {ftp://ftp.informatik.uni-freiburg.de/papers/lmb/Haasdonk2002_Tangent_Distance_Kernels_for_SVM.pdf}}, owner = {haasdonk}, pages = {864-868}, publisher = {IEEE Computer Society}, title = {Tangent Distance Kernels for Support Vector Machines}, volume = 2, year = 2002 }
2001
1. B. Haasdonk, D. Kröner, and C. Rohde, “Convergence of a staggered Lax-Friedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids,” Numer. Math., vol. 88, no. 3, Art. no. 3, 2001, doi: 10.1007/s211-001-8011-x.
  - BibTeX
  BibTeX
  @article{haasdonk2001convergence, author = {Haasdonk, B. and Kröner, D. and Rohde, C.}, coden = {NUMMA7}, doi = {10.1007/s211-001-8011-x}, file = {:/afs/.mathe/public/www/ians/am/Haasdonk/publications/HKR01.pdf:PDF}, fjournal = {Numerische Mathematik}, issn = {0029-599X}, journal = {Numer. Math.}, mrclass = {65M06}, mrnumber = {1835467 (2002c:65133)}, mrreviewer = {Kenneth H. Karlsen}, number = 3, owner = {szur}, pages = {459--484}, title = {Convergence of a staggered {L}ax-{F}riedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids}, volume = 88, year = 2001 }
2. B. Haasdonk, M. Ohlberger, M. Rumpf, A. Schmidt, and K.-G. Siebert, “h-p-Multiresolution Visualization of Adaptive Finite Element Simulations,” Mathematics Department, University of Freiburg, Preprint 01-26, 2001.
  - BibTeX
  BibTeX
  @techreport{Haasdonk2001c, author = {Haasdonk, Bernard and Ohlberger, M. and Rumpf, M. and Schmidt, A. and Siebert, K.-G.}, file = {:PDF/Haasdonk2001c_www_h_p_vis_grape_preprint.pdf:PDF}, groups = {haasdonk_misc, haasdonk_all_papers}, institution = {Mathematics Department, University of Freiburg}, number = {Preprint 01-26}, owner = {haasdonk}, title = {h-p-Multiresolution Visualization of Adaptive Finite Element Simulations}, year = 2001 }
3. B. Haasdonk, D. Kröner, and C. Rohde, “Convergence of a staggered Lax-Friedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids,” Numer. Math., vol. 88, no. 3, Art. no. 3, 2001, doi: 10.1007/s211-001-8011-x.
  - BibTeX
  - Link
  BibTeX
  @article{Haasdonk2001a, author = {Haasdonk, Bernard and Kr{\"o}ner, D. and Rohde, C.}, coden = {NUMMA7}, doi = {10.1007/s211-001-8011-x}, file = {:PDF/Haasdonk2001a_www_preprint_StgLxF_convergence.pdf:PDF;:PDF/Haasdonk2001a_convergence_StgLxF_Numerische_Mathematik.pdf:PDF}, fjournal = {Numerische Mathematik}, groups = {haasdonk, haasdonk_all_papers}, issn = {0029-599X}, journal = {Numer. Math.}, mrclass = {65M06}, mrnumber = {MR1835467 (2002c:65133)}, mrreviewer = {Kenneth H. Karlsen}, number = 3, owner = {haasdonk}, pages = {459--484}, title = {Convergence of a staggered {L}ax-{F}riedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids}, url = {http://dx.doi.org/10.1007/s211-001-8011-x}, volume = 88, year = 2001 }
  Link
  http://dx.doi.org/10.1007/s211-001-8011-x
2000
1. B. Haasdonk, “Convergence of a Staggered Lax-Friedrichs Scheme on Unstructured 2D-Grids,” in HYP 2000, Proceedings of the 8th International Conference on Hyperbolic Problems, 2000, vol. 2, pp. 475--484.
  - BibTeX
  BibTeX
  @inproceedings{haasdonk2000convergence, author = {Haasdonk, B.}, booktitle = {HYP 2000, Proceedings of the 8th International Conference on Hyperbolic Problems}, owner = {haasdonk}, pages = {475--484}, publisher = {Birkh�user}, title = {Convergence of a Staggered {L}ax-{F}riedrichs Scheme on Unstructured 2D-Grids}, volume = 2, year = 2000 }
1999
1. T. Ge\sner et al., “A Procedural Interface for Multiresolutional Visualization of General Numerical Data,” University of Bonn, SFB 256 Report 28, 1999.
  - BibTeX
  BibTeX
  @techreport{gessner1999procedural, author = {Ge{\s}ner, T. and Haasdonk, B. and Lenz, M. and Metscher, M. and Neubauer, R. and Ohlberger, M. and Rosenbaum, W. and Rumpf, M. and Schw\"orer, R. and Spielberg, M. and Weikard, U.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Gessner1999_www_Grape_preprint.pdf:PDF}, institution = {University of Bonn}, number = 28, owner = {haasdonk}, title = {A Procedural Interface for Multiresolutional Visualization of General Numerical Data}, type = {SFB 256 Report}, year = 1999 }
2. T. Geßner et al., “A Procedural Interface for Multiresolutional Visualization of General Numerical Data,” University of Bonn, SFB 256 Report 28, 1999.
  - BibTeX
  BibTeX
  @techreport{Gessner1999, author = {Ge{\ss}ner, T. and Haasdonk, Bernard and Lenz, M. and Metscher, M. and Neubauer, R. and Ohlberger, M. and Rosenbaum, W. and Rumpf, M. and Schw{\"o}rer, R. and Spielberg, M. and Weikard, U.}, file = {:PDF/Gessner1999_www_Grape_preprint.pdf:PDF}, groups = {haasdonk_misc, haasdonk_all_papers}, institution = {University of Bonn}, number = 28, owner = {haasdonk}, title = {A Procedural Interface for Multiresolutional Visualization of General Numerical Data}, type = {SFB 256 Report}, year = 1999 }
3. B. Haasdonk, “Konvergenz eines Staggered Lax-Friedrichs Verfahrens auf unstrukturierten 2D Gittern,” 1999.
  - BibTeX
  BibTeX
  @mastersthesis{Haasdonk1999, author = {Haasdonk, Bernard}, file = {:PDF/Haasdonk1999_www_Diplomarbeit_Uni_Freiburg.pdf:PDF}, groups = {haasdonk, haasdonk_all_papers}, owner = {haasdonk}, school = {Universit{\"a}t Freiburg, Abteilung f{\"u}r Angewandte Mathematik}, title = {Konvergenz eines Staggered {L}ax-{F}riedrichs {V}erfahrens auf unstrukturierten 2D {G}ittern}, year = 1999 }

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