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Publications

Publications of our group

Note

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

Publications

2019
1. M. Köppel et al., “Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario,” Computers & Geosciences, vol. 2, no. 23, pp. 339–354, 2019.
  - BibTeX
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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 = {Computers & Geosciences}, 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 = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1759}, volume = 2, year = 2019 }
2018
1. B. M. Afkham, A. Bhatt, B. Haasdonk, and J. S. Hesthaven, “Symplectic Model-Reduction with a Weighted Inner Product,” 2018.
  - BibTeX
  @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. T. Brünnette, G. Santin, and B. Haasdonk, “Greedy kernel methods for accelerating implicit integrators for parametric ODEs,” 2018, vol. Proceedings of ENUMATH 2017.
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  @inproceedings{brunnette2018greedy, 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}, 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}, volume = {Proceedings of ENUMATH 2017}, year = 2018 }
3. 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, 2018.
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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 }
4. 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.
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  @inbook{haasdonk2018greedy, 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}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/HS2017_www_preprint.pdf:PDF}, 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 }
5. D. Wittwar and B. Haasdonk, “Greedy Algorithms for Matrix-Valued Kernels,” University of Stuttgart, 2018.
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  @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 }
2017
1. 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.
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  @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 }
2. C. Dibak, A. Schmidt, F. Dürr, B. Haasdonk, and K. Rothermel, “Server-Assisted Interactive Mobile Simulations for Pervasive Applications,” in Proceedings of the 15th IEEE International Conference on Pervasive Computing and Communications (PerCom), Kona, Hawaii, USA, 2017, pp. 1--10.
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  @inproceedings{dibak2017serverassisted, 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 mobile device and a remote server. For the computation of parameter-dependent solutions of the simulation, we use the reduced basis method, which allows to drastically reduce the computation time and energy consumption. We present three approaches for the distributed execution of the reduced basis method between mobile device and server. Evaluations show that we can speed-up the numerical computation to over 131 times while using 73 times less energy compared to offloading everything to a server.}, address = {Kona, Hawaii, USA}, author = {Dibak, Christoph and Schmidt, Andreas and D{\"u}rr, Frank and Haasdonk, Bernard and Rothermel, Kurt}, booktitle = {Proceedings of the 15th IEEE International Conference on Pervasive Computing and Communications (PerCom)}, contact = {Christoph Dibak christoph.dibak@ipvs.uni-stuttgart.de}, cr-category = {C.2.4 Distributed Systems, G.1 Numerical Analysis}, department = {University of Stuttgart, Institute of Parallel and Distributed Systems, Distributed Systems}, ee = {ftp://ftp.informatik.uni-stuttgart.de/pub/library/ncstrl.ustuttgart_fi/INPROC-2017-02/INPROC-2017-02.pdf}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Dibak2017_www_server_assisted.pdf:PDF}, institution = {University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology, Germany}, language = {English}, month = {March}, owner = {schmidta}, pages = {1--10}, publisher = {IEEE}, title = {{Server-Assisted Interactive Mobile Simulations for Pervasive Applications}}, type = {Conference Paper}, url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2017-02&engl=1}, year = 2017 }
3. 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.
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  @incollection{haasdonk2017reduced, author = {Haasdonk, B.}, booktitle = {Model Reduction and Approximation: Theory and Algorithms}, editor = {Benner, P. and Cohen, A. and Ohlberger, M. and Willcox, K.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Haasdonk2014a_www_preprint_RBtutorial_with_update2016.pdf:PDF}, 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 }
4. 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, 2017.
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  @article{martini2017certified, author = {Martini, I. and Rozza, G. and Haasdonk, B.}, doi = {10.1007/s10915-017-0430-y}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Martini2015_www_RB_viscous_inviscid_coupling.pdf:PDF}, journal = {Journal of Scientific Computing}, owner = {maieril}, 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}, year = 2017 }
5. G. Santin and B. Haasdonk, “Convergence rate of the data-independent P-greedy algorithm in kernel-based approximation,” Dolomites Research Notes on Approximation, vol. 10, pp. 68--78, 2017.
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  @article{santin2017convergence, 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 samples� 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, B.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/SH16b_www_p-greedy.pdf:PDF}, journal = {Dolomites Research Notes on Approximation}, owner = {haasdonk}, pages = {68--78}, title = {Convergence rate of the data-independent {P}-greedy algorithm in kernel-based approximation}, url = {http://www.emis.de/journals/DRNA/9-2.html}, volume = 10, year = 2017 }
6. A. Schmidt and B. Haasdonk, “Data-driven surrogates of value functions and applications to feedback control for dynamical systems,” University of Stuttgart, 2017.
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  @techreport{schmidt2017datadriven, author = {Schmidt, A. and Haasdonk, B.}, 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=1742}, year = 2017 }
7. A. Schmidt and B. Haasdonk, “Reduced basis approximation of large scale parametric algebraic Riccati equations,” ESAIM: Control, Optimisation and Calculus of Variations, 2017.
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  @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 = feb, 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 }
8. 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.
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  @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 = jul, 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 }
9. D. Wittwar, A. Schmidt, and B. Haasdonk, “Reduced Basis Approximation for the Discrete-time Parametric Algebraic Riccati Equation,” University of Stuttgart, 2017.
  - 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. 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, 2016.
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  @article{amsallem2016peblrom, author = {Amsallem, D. and Haasdonk, B.}, doi = {10.1186/s40323-016-0059-7}, journal = {AMSES, Advanced Modeling and Simulation in Engineering Sciences}, number = 6, owner = {santinge}, 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 }
2. A. C. Antoulas, B. Haasdonk, and B. Peherstorfer, MORML 2016 Book of Abstracts. University of Stuttgart, 2016.
  - BibTeX
  @book{antoulas2016morml, author = {Antoulas, A. C. and Haasdonk, B. and Peherstorfer, B.}, owner = {haasdonk}, publisher = {University of Stuttgart}, title = {MORML 2016 Book of Abstracts}, year = 2016 }
3. 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.
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  @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 }
4. K. Carlberg, L. Brencher, B. Haasdonk, and A. Barth, “Data-driven time parallelism via forecasting,” 2016.
  - BibTeX
  @unpublished{carlberg2016datadriven, author = {Carlberg, Kevin and Brencher, Lukas and Haasdonk, Bernard and Barth, Andrea}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/CBHB16_www_arxiv_forecasting_time_parallelization.pdf:PDF}, language = {English}, note = {submitted to SIAM J. of Sci. Comp.}, owner = {seusdd}, title = {Data-driven time parallelism via forecasting}, year = 2016 }
5. 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, 2016.
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  @techreport{fritzen2016algorithmic, author = {Fritzen, Felix and Haasdonk, Bernard and Ryckelynck, David and Schöps, Sebastian}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/FHRS16_www_CoSiMoR_Preprint_2016.pdf:PDF}, 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 }
6. D. Garmatter, B. Haasdonk, and B. Harrach, “A reduced Landweber Method for Nonlinear Inverse Problems,” Inverse Problems, vol. 32, no. 3, pp. 1--21, 2016.
  - BibTeX
  @article{garmatter2016reduced, author = {Garmatter, D. and Haasdonk, B. and Harrach, B.}, doi = {http://dx.doi.org/10.1088/0266-5611/32/3/035001}, journal = {Inverse Problems}, number = 3, owner = {santinge}, pages = {1--21}, title = {A reduced {L}andweber Method for Nonlinear Inverse Problems}, volume = 32, year = 2016 }
7. 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, 2016.
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  @article{redeker2016podeim, author = {Redeker, M. and Haasdonk, B.}, doi = {10.1080/13873954.2016.1198384}, journal = {MCMDS, Mathematical and Computer Modelling of Dynamical Systems}, owner = {santinge}, 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}, year = 2016 }
2015
1. D. Amsallem, C. Farhat, and B. Haasdonk, “Editorial: Special Issue on Modelling Reduction,” IJNME, International Journal of Numerical Methods in Engineering, vol. 102, no. 5, pp. 931--932, 2015.
  - BibTeX
  @article{amsallem2015editorial, 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 = {Editorial: Special Issue on Modelling Reduction}, volume = 102, year = 2015 }
2. 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), no. 1408.1220, 2015.
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  @article{burkovska2015reduced, author = {Burkovska, O. and Haasdonk, B. and Salomon, J. and Wohlmuth, B.}, institution = {Arxiv}, journal = {SIAM journal on Financial Mathematics (SIFIN)}, note = {in press}, 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 = 2015 }
3. M. Dihlmann and B. Haasdonk, “A reduced basis Kalman filter for parametrized partial differential equations,” ESAIM: Control, Optimisation and Calculus of Variations, 2015.
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  @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 }
4. 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, pp. 753--787, 2015.
  - BibTeX
  @article{dihlmann2015certified, author = {Dihlmann, M. A. and Haasdonk, B.}, doi = {DOI: 10.1007/s10589-014-9697-1}, 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 }
5. 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.
  - 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 }
6. 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.
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  @inproceedings{martini2015output, author = {Martini, I. and Haasdonk, B.}, booktitle = {Numerical Mathematics and Advanced Applications - ENUMATH 2013}, doi = {10.1007/978-3-319-10705-9_43}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Maier2013a_www_RB_homogeneous_DD_output_bounds.pdf:PDF}, 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 }
7. 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.
  - BibTeX
  - Link
  @inproceedings{schmidt2015basis, author = {Schmidt, A. and Dihlmann, M. and Haasdonk, B.}, booktitle = {Proc. MATHMOD 2015 - 8th Vienna International Conference on Mathematical Modelling}, doi = {10.1016/j.ifacol.2015.05.016}, owner = {schmidta}, pages = {713--718}, qualityassured = {qualityAssured}, 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 }
8. 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, pp. 1--28, 2015.
  - 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 }
2014
1. B. Haasdonk, “Reduced Basis Methods for Parametrized PDEs -- A Tutorial Introduction for Stationary and Instationary Problems,” IANS, University of Stuttgart, Germany, 2014.
  - BibTeX
  - Link
  @techreport{haasdonk2014reduced, author = {Haasdonk, B.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Haasdonk2014a_www_preprint_RBtutorial_with_update2016.pdf:PDF}, institution = {IANS, University of Stuttgart, Germany}, note = {Chapter in P. Benner, A. Cohen, M. Ohlberger 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 }
2. 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, pp. 6–13, 2014.
  - 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 }
3. 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,” arXiv.org, 2014.
  - BibTeX
  - Link
  @article{kaulmann2014localized, abstract = {In this work, we propose a novel model order reduction approach for two-phase flow in porous media by introducing a formulation in which the mobility, which realizes the coupling between phase saturations and phase pressures, is regarded as a parameter to the pressure equation. Using this formulation, we introduce the Localized Reduced Basis Multiscale method to obtain a low-dimensional surrogate of the high-dimensional pressure equation. By applying ideas from model order reduction for parametrized partial differential equations, we are able to split the computational effort for solving the pressure equation into a costly offline step that is performed only once and an inexpensive online step that is carried out in every time step of the two-phase flow simulation, which is thereby largely accelerated. Usage of elements from numerical multiscale methods allows us to displace the computational intensity between the offline and online step to reach an ideal runtime at acceptable error increase for the two-phase flow simulation.}, author = {Kaulmann, Sven and Flemisch, Bernd and Haasdonk, Bernard and Lie, Knut-Andreas and Ohlberger, Mario}, date-added = {2014-05-13T14:44:03GMT}, date-modified = {2014-05-14T09:53:22GMT}, eprint = {1405.2810v1}, eprintclass = {math.NA}, eprinttype = {arxiv}, file = {Kaulmann2014wa.pdf:/fak8/ians/publications/files/Kaulmann2014wa.pdf:PDF}, journal = {arXiv.org}, month = may, owner = {kaulmann}, rating = {0}, read = {Yes}, title = {{The Localized Reduced Basis Multiscale method for two-phase flows in porous media}}, url = {http://arxiv.org/abs/1405.2810v1}, year = 2014 }
4. 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.
  - BibTeX
  - Link
  @article{maier2014dirichletneumann, author = {Maier, I. and Haasdonk, B.}, doi = {10.1016/j.apnum.2013.12.001}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Maier2014_www_preprint_RB_homogeneous_domain_decomposition.pdf:PDF}, 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 }
5. D. Wirtz, D. C. Sorensen, and B. Haasdonk, “A Posteriori Error Estimation for DEIM Reduced Nonlinear Dynamical Systems,” SIAM Journal on Scientific Computing, vol. 36, no. 2, pp. A311--A338, 2014.
  - BibTeX
  - Link
  @article{wirtz2014posteriori, author = {Wirtz, D. and Sorensen, D.C. and Haasdonk, B.}, doi = {10.1137/120899042}, eprint = {http://dx.doi.org/10.1137/120899042}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/WSH14_www_WSH12_preprint_version.pdf:PDF}, journal = {SIAM Journal on Scientific Computing}, number = 2, owner = {schmidta}, pages = {A311--A338}, publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})}, qualityassured = {qualityAssured}, title = {A Posteriori Error Estimation for {DEIM} Reduced Nonlinear Dynamical Systems}, url = {http://dx.doi.org/10.1137/120899042}, volume = 36, year = 2014 }
2013
1. D. Amsallem, B. Haasdonk, and G. Rozza, “A Conference within a Conference for MOR Researchers,” SIAM News, vol. 46, no. 6, p. 8, 2013.
  - BibTeX
  - Link
  @article{amsallem2013conference, author = {Amsallem, D. and Haasdonk, B. and Rozza, G.}, journal = {SIAM News}, month = {July/August}, 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 }
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. Cvetkovic, T. Atanackovic and V. Kostic, vol. 13, no. 1, pp. 3–6, 2013.
  - BibTeX
  @article{dihlmann2013certified, author = {Dihlmann, M and Haasdonk, B.}, doi = {doi: 10.1002/pamm.201310002}, 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. Cvetkovic, T. Atanackovic and V. Kostic}, 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), 2013.
  - 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, pp. 501–519, 2013.
  - BibTeX
  - Link
  @article{fehr2013greedybased, author = {Fehr, J. and Fischer, M. and Haasdonk, B. and Eberhard, P.}, doi = {10.1002/zamm.201200014}, 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 }
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
  @article{haasdonk2013reduced, author = {Haasdonk, B. and Urban, K. and Wieland, B.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Haasdonk2013_www_preprint_HUW2012_RB_stochastic_PDEs.pdf:PDF}, 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, pp. 859--873, 2013.
  - BibTeX
  - Link
  @article{haasdonk2013convergence, 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, B.}, doi = {10.1051/m2an/2012045}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/H13_www_preprint_POD_Greedy_Convergence.pdf:PDF}, journal = {{ESAIM}: Mathematical Modelling and Numerical Analysis}, number = 3, owner = {schmidta}, pages = {859--873}, publisher = {{EDP} Sciences}, qualityassured = {qualityAssured}, title = {Convergence Rates of the {POD}--{G}reedy Method}, url = {http://dx.doi.org/10.1051/m2an/2012045}, volume = 47, year = 2013 }
7. S. Kaulmann and B. Haasdonk, “Online Greedy Reduced Basis Construction Using Dictionaries,” in VI International Conference on Adaptive Modeling and Simulation (ADMOS 2013), Lisbon, Portugal, 2013, pp. 365--376.
  - BibTeX
  - Link
  @inproceedings{kaulmann2013online, abstract = {The Reduced Basis method is a means for model order reduction for parametrized partial differential equations. In the last decades it has found broad application for problems with multi-query or real-time character. While the method has shown to be performing well for numerous different fields of applications, problems with high parameter dimension or high sensitivity with respect to the parameter still pose major challenges. In our contribution, we present a new basis generation algorithm that is particularly fit to these kinds of problems: Instead of building the reduced basis during the offline phase we build a large dictionary of basis vector candidates and compute a small parameter-adapted basis from that dictionary with a Greedy procedure during the online phase.}, address = {Lisbon, Portugal}, author = {Kaulmann, Sven and Haasdonk, Bernard}, booktitle = {VI International Conference on Adaptive Modeling and Simulation (ADMOS 2013)}, date-added = {2014-01-07T08:14:37GMT}, date-modified = {2014-06-03T08:55:20GMT}, editor = {Moitinho de Almeida, Jos{\'e} Paulo Baptista and D{\'\i}ez, Pedro and Tiago, Carlos and Par{\'e}s, N{\'u}ria}, month = may, owner = {kaulmann}, pages = {365--376}, rating = {0}, read = {Yes}, title = {{Online Greedy Reduced Basis Construction Using Dictionaries}}, url = {http://www.lacan.upc.edu/admos2013/Proceedings.html}, 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.
  - BibTeX
  - Link
  @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 }
9. D. Wirtz and B. Haasdonk, “A Vectorial Kernel Orthogonal Greedy Algorithm,” Dolomites Res. Notes Approx., vol. 6, pp. 83–100, 2013.
  - BibTeX
  - Link
  @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 }
2012
1. F. Albrecht, B. Haasdonk, S. Kaulmann, and M. Ohlberger, “The Localized Reduced Basis Multiscale Method,” in Algoritmy 2012, 2012, pp. 393--403.
  - BibTeX
  - Link
  @inproceedings{albrecht2012localized, abstract = {In this paper we introduce the Localized Reduced Basis Multiscale (LRBMS) method for parameter dependent heterogeneous elliptic multiscale problems. The LRBMS method brings together ideas from both Reduced Basis methods to efficiently solve parametrized problems and from multiscale methods in order to deal with complex heterogeneities and large domains. Experiments on 2D and real world 3D data demonstrate the performance of the approach.}, affiliation = {Slovak University of Technology in Bratislava}, author = {Albrecht, Felix and Haasdonk, Bernard and Kaulmann, Sven and Ohlberger, Mario}, booktitle = {Algoritmy 2012}, date-added = {2012-10-24T14:53:21GMT}, date-modified = {2014-05-14T09:52:11GMT}, editor = {Handlovi{\v c}ov{\'a}, Angela and Minarechov{\'a}, Zuzana and {\v S}ev{\v c}ovi{\v c}, Daniel}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Albrecht2012_www_LRBMS_method_Algoritmy_Proceedings.pdf:PDF}, month = apr, organization = {Slovak University of Technology in Bratislava}, owner = {kaulmann}, pages = {393--403}, publisher = {Publishing House of STU}, rating = {0}, read = {Yes}, title = {{The Localized Reduced Basis Multiscale Method}}, url = {http://www.iam.fmph.uniba.sk/algoritmy2012/}, year = 2012 }
2. M. Dihlmann, S. Kaulmann, and B. Haasdonk, “Online Reduced Basis Construction Procedure for Model Reduction of Parametrized Evolution Systems,” in Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling, 2012.
  - BibTeX
  @inproceedings{dihlmann2012online, author = {Dihlmann, M. and Kaulmann, S. and Haasdonk, B.}, booktitle = {Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Dihlmann2012_www_Mathmod2012_online_greedy_evolution_RB.pdf:PDF}, 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,” in Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling, 2012.
  - BibTeX
  - Link
  @inproceedings{drohmann2012reduced, author = {Drohmann, M. and Haasdonk, B. 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}, 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 }
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, pp. A937–A969, 2012.
  - BibTeX
  @article{drohmann2012reduced, 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 Fr�chet 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, B. and Ohlberger, M.}, doi = {10.1137/10081157X}, eprint = {http://epubs.siam.org/doi/pdf/10.1137/10081157X}, 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.
  - BibTeX
  - Link
  @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 = apr, 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 }
6. B. Haasdonk, J. Salomon, and B. Wohlmuth, “A Reduced Basis Method for the Simulation of American Options,” in ENUMATH 2011 Proceedings, 2012.
  - BibTeX
  - Link
  @inproceedings{haasdonk2012reduced, author = {Haasdonk, B. and Salomon, J. and Wohlmuth, B.}, booktitle = {ENUMATH 2011 Proceedings}, owner = {haasdonk}, title = {A Reduced Basis Method for the Simulation of {A}merican Options}, url = {http://arxiv.org/pdf/1201.3289v1}, year = 2012 }
7. B. Haasdonk, J. Salomon, and B. Wohlmuth, “A Reduced Basis Method for Parametrized Variational Inequalities,” University of Stuttgart, 2012.
  - BibTeX
  @techreport{haasdonk2012reduced, author = {Haasdonk, B. and Salomon, J. and Wohlmuth, B.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/HSW12_www_pre.pdf:PDF}, institution = {University of Stuttgart}, owner = {haasdonk}, title = {A Reduced Basis Method for Parametrized Variational Inequalities}, type = {{S}im{T}ech Preprint}, 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
  @article{ruiner2012aposteriori, author = {Ruiner, T. and Fehr, J. and Haasdonk, B. and Eberhard, P.}, 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.
  - BibTeX
  - Link
  @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 }
10. D. Wirtz and B. Haasdonk, “An Improved Vectorial Kernel Orthogonal Greedy Algorithm,” University of Stuttgart, 2012.
  - BibTeX
  - Link
  @techreport{wirtz2012improved, 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}, institution = {University of Stuttgart}, note = {{I}n preparation}, 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 }
11. D. Wirtz, D. C. Sorensen, and B. Haasdonk, “A-posteriori error estimation for DEIM reduced nonlinear dynamical systems,” University of Stuttgart, 2012.
  - BibTeX
  - Link
  @techreport{wirtz2012aposteriori, 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 = {:/home/dwirtz/dwirtzwww/WSH12_pre.pdf:PDF}, institution = {University of Stuttgart}, month = oct, note = {Submitted to SISC}, 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 }
12. D. Wirtz, N. Karajan, and B. Haasdonk, “Model order reduction of multiscale models using kernel methods,” SRC SimTech, University of Stuttgart, Germany, 2012.
  - 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 = {June}, note = {Submitted}, owner = {dwirtz}, title = {Model order reduction of multiscale models using kernel methods}, type = {Preprint}, year = 2012 }
2011
1. M. Dihlmann, M. Drohmann, and B. Haasdonk, “Model Reduction of Parametrized Evolution Problems using the Reduced basis Method with Adaptive Time-Partitioning,” in Proc. of ADMOS 2011, 2011.
  - BibTeX
  @inproceedings{dihlmann2011model, author = {Dihlmann, M. and Drohmann, M. and Haasdonk, B.}, booktitle = {Proc. of ADMOS 2011}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/DDH11_www_preprint_Tpart_ADMOS2011.pdf:PDF}, 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,” in In Proc. FVCA6, 2011.
  - BibTeX
  @inproceedings{drohmann2011adaptive, author = {Drohmann, M. and Haasdonk, B. and Ohlberger, M.}, booktitle = {In Proc. FVCA6}, 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
  @article{haasdonk2011training, author = {Haasdonk, B. and Dihlmann, M. and Ohlberger, M.}, journal = {Mathematical and Computer Modelling of Dynamical Systems}, owner = {schmidta}, pages = {423--442}, qualityassured = {qualityAssured}, 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, 2011–004, 2011.
  - BibTeX
  @techreport{haasdonk2011reduziertebasismethoden, author = {Haasdonk, B.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Haasdonk2011c_www_rb_lecture_script_IANS_report_0411.pdf:PDF}, 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, pp. 295--296, 2011.
  - BibTeX
  - Link
  @article{haasdonk2011special, author = {Haasdonk, B. and Lohmann, B.}, doi = {10.1080/13873954.2011.547661}, 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 }
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, pp. 145--161, 2011.
  - BibTeX
  - Link
  @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 }
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, pp. 561--582, 2011.
  - BibTeX
  - Link
  @article{jung2011model, author = {Jung, N. and Patera, A.T. and Haasdonk, B. and Lohmann, B.}, doi = {10.1080/13873954.2011.582120}, 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 }
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, pp. 1233--1238, 2011.
  - BibTeX
  - Link
  @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 = dec, 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 }
2010
1. B. Haasdonk, “Effiziente und Gesicherte Modellreduktion f�r Parametrisierte Dynamische Systeme.,” at - Automatisierungstechnik, vol. 58, no. 8, pp. 468--474, 2010.
  - BibTeX
  @article{haasdonk2010effiziente, author = {Haasdonk, B.}, journal = {at - Automatisierungstechnik}, number = 8, owner = {haasdonk}, pages = {468--474}, title = {Effiziente und Gesicherte {M}odellreduktion f�r Parametrisierte Dynamische {S}ysteme.}, volume = 58, year = 2010 }
2. E. Pekalska and B. Haasdonk, “Indefinite Kernel Discriminant Analysis,” in Proc. COMPSTAT 2010, International Conference on Computational Statistics, 2010.
  - BibTeX
  @inproceedings{pekalska2010indefinite, author = {Pekalska, E. and Haasdonk, B.}, booktitle = {Proc. COMPSTAT 2010, International Conference on Computational Statistics}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Pekalska2010_www_COMPSTAT2010.pdf:PDF}, owner = {haasdonk}, title = {Indefinite Kernel Discriminant Analysis}, year = 2010 }
2009
1. B. Haasdonk, M. Ohlberger, T. Tonn, and K. Urban, MoRePaS 2009 Book of Abstracts. University of M�nster, 2009.
  - BibTeX
  @book{haasdonk2009morepas, author = {Haasdonk, B. and Ohlberger, M. and Tonn, T. and Urban, K.}, owner = {haasdonk}, publisher = {University of M�nster}, title = {MoRePaS 2009 Book of Abstracts}, year = 2009 }
2. B. Haasdonk and M. Ohlberger, “Efficient a-posteriori Error Estimation for Parametrized Reduced Dynamical Systems,” in GMA-Fachaussschuss 1.30, Tagungsband, 2009.
  - 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 }
3. B. Haasdonk and M. Ohlberger, “Space-Adaptive Reduced Basis Simulation for Time-Dependent Problems,” in Proc. MATHMOD 2009, 6th Vienna International Conference on Mathematical Modelling, 2009.
  - BibTeX
  - Link
  @inproceedings{haasdonk2009spaceadaptive, author = {Haasdonk, B. and Ohlberger, M.}, booktitle = {Proc. MATHMOD 2009, 6th Vienna International Conference on Mathematical Modelling}, 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 }
4. B. Haasdonk and M. Ohlberger, “Efficient Reduced Models for Parametrized Dynamical Systems by Offline/Online Decomposition,” in Proc. MATHMOD 2009, 6th Vienna International Conference on Mathematical Modelling, 2009.
  - BibTeX
  - Link
  @inproceedings{haasdonk2009efficient, author = {Haasdonk, B. and Ohlberger, M.}, booktitle = {Proc. MATHMOD 2009, 6th Vienna International Conference on Mathematical Modelling}, 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 }
5. 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
  @incollection{haasdonk2009reduced, address = {Providence, RI}, author = {Haasdonk, B. and Ohlberger, M.}, booktitle = {Hyperbolic problems: theory, numerics and applications}, 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 }
6. N. Jung, B. Haasdonk, and D. Kröner, “Reduced Basis Method for Quadratically Nonlinear Transport Equations,” IJCSM, vol. 2, no. 4, pp. 334–353, 2009.
  - BibTeX
  @article{jung2009reduced, annote = {Available as SimTech Preprint 2009-15.}, author = {Jung, N. and Haasdonk, B. and Kr{\"o}ner, D.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Jung2009_www_RB_quadratically_nonlinear_PDEs_preprint.pdf:PDF}, journal = {IJCSM}, number = 4, owner = {haasdonk}, pages = {334-353}, title = {Reduced Basis Method for Quadratically Nonlinear Transport Equations}, type = {Preprint SimTech}, volume = 2, year = 2009 }
7. 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, pp. 1017–1032, 2009.
  - BibTeX
  @article{pekalska2009kernel, author = {Pekalska, E. and Haasdonk, B.}, 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.
  - BibTeX
  - Link
  @inproceedings{drohmann2008reduced, author = {Drohmann, M. and Haasdonk, B. and Ohlberger, M.}, booktitle = {Proceedings of ALGORITMY 2009}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/DHO08_www_algorithmy_geometry_parameters_RB.pdf:PDF}, 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 }
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
  @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,” in Proc. ICPR 2008, International Conference on Pattern Recognition, 2008.
  - 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, pp. 277--302, 2008.
  - BibTeX
  - Link
  @article{haasdonk2008reduced, author = {Haasdonk, B. and Ohlberger, M.}, doi = {10.1051/m2an:2008001}, journal = {ESAIM: M2AN}, month = {March}, number = 2, owner = {santinge}, 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 }
5. B. Haasdonk and E. Pekalska, “Classification with Kernel Mahalanobis Distances,” in Proc. of 32nd. GfKl Conference, Advances in Data Analysis, Data Handling and Business Intelligence, 2008.
  - BibTeX
  @inproceedings{haasdonk2008classification, author = {Haasdonk, B. and Pekalska, E.}, booktitle = {Proc. of 32nd. GfKl Conference, Advances in Data Analysis, Data Handling and Business Intelligence}, 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.
  - BibTeX
  - Link
  @article{haasdonk2008reduced, author = {Haasdonk, B. and Ohlberger, M. and Rozza, G.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/HOR08_www_preprint_EOI_explicit_operators_before_ETNA.pdf:PDF}, 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 }
7. E. Pekalska and B. Haasdonk, “Kernel Quadratic Discriminant Analysis with Positive and Indefinite Kernels,” University of Münster, 06/08, 2008.
  - BibTeX
  @techreport{pekalska2008kernel, author = {Pekalska, E. and Haasdonk, B.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Pekalska2008a_www_preprint_Kernel_Quad_Discr_Analysis_Positive_Indefinite_Kernels.pdf:PDF}, institution = {University of Münster}, 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
  @article{fuhrmann2007guest, author = {Fuhrmann, J. and Haasdonk, B. and Holzbecher, E. and Ohlberger, M.}, 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, 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
  @techreport{haasdonk2007reduced, 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 ?nite element schemes. Due to the characteristic of?ine-online decomposition, the reduced models often become suitable for a multi-query or real-time setting, where simulation results, such as ?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 of?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 quanti?cation of the resulting reduced simulation error. Numerical experiments on a parametrized convection problem, discretized with a ?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, B. and Ohlberger, M. and Rozza, G.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/HOR07_www_preprint_EOI_explicit_operators_before_ETNA.pdf:PDF}, 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 }
3. 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
  @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 }
4. B. Haasdonk and H. Burkhardt, “Invariant Kernels for Pattern Analysis and Machine Learning,” Machine Learning, vol. 68, pp. 35--61, 2007.
  - BibTeX
  @article{haasdonk2007invariant, author = {Haasdonk, B. and Burkhardt, H.}, doi = {DOI 10.1007/s10994-007-5009-7}, institution = {IIF-LMB, Universit�t Freiburg, Institut f�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,” in Proc. of 31st GfKl Conference, Data Analysis, Machine Learning, and Applications, 2007.
  - BibTeX
  @inproceedings{haasdonk2007classification, author = {Haasdonk, B. and Burkhardt, H.}, booktitle = {Proc. of 31st GfKl Conference, Data Analysis, Machine Learning, and Applications}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Haasdonk2007b_www_classification_invariant_kernels_GfKl2007.pdf:PDF}, 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
  @techreport{haasdonk2006reduced, author = {Haasdonk, B. and Ohlberger, M.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Haasdonk2006b_www_RB_lin_FV_preprint_before_M2AN.pdf:PDF}, institution = {University of Freiburg, Institute of Applied Mathematics}, note = {Extended version of M2AN article.}, number = {12/2006}, owner = {bhaas_01}, title = {Reduced Basis Method for Finite Volume Approximations of Parametrized Evolution Equations}, year = 2006 }
2. 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
  @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, “Transformation Knowledge in Pattern Analysis with Kernel Methods, Distance and Integration Kernels,” PhD dissertation, Albert-Ludwigs-Universität, Freiburg im Breisgau, Fakultät für Angewandte Wissenschaften, 2005.
  - BibTeX
  @phdthesis{haasdonk2005transformation, author = {Haasdonk, B.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Ha05_www_Dissertation_Uni_Freiburg.pdf:PDF}, 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\"at, Freiburg im Breisgau, Fakult\"at für Angewandte Wissenschaften}, title = {Transformation Knowledge in Pattern Analysis with Kernel Methods, Distance and Integration Kernels}, year = 2005 }
2. B. Haasdonk, “Feature Space Interpretation of SVMs with Indefinite Kernels,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 4, pp. 482–492, 2005.
  - BibTeX
  @article{haasdonk2005feature, address = {Los Alamitos, CA, USA}, author = {Haasdonk, B.}, doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2005.78}, issn = {0162-8828}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, number = 4, owner = {santinge}, pages = {482-492}, publisher = {IEEE Computer Society}, title = {Feature Space Interpretation of {SVMs} with Indefinite Kernels}, volume = 27, year = 2005 }
3. B. Haasdonk, A. Vossen, and H. Burkhardt, “Invariance in Kernel Methods by Haar-Integration Kernels,” in Proceedings of the 14th Scandinavian Conference on Image Analysis, 2005.
  - 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 }
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
  @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.
  - BibTeX
  @inproceedings{haasdonk2004adjustable, author = {Haasdonk, B. 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}, number = 2, owner = {santinge}, 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
  @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, Universit�t Freiburg, 2/03, 2003.
  - BibTeX
  @techreport{haasdonk2003prestobox, author = {Haasdonk, B. and Poluru, B.R. and Teynor, A.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Haasdonk2003_www_prestobox_documentation_techrep_uni_freiburg.pdf:PDF}, institution = {IIF-LMB, Universit�t Freiburg}, month = {November}, 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, no. 3, pp. 181–204, 2003.
  - BibTeX
  @article{haasdonk2003multiresolution, abstract = {h�p�adaptive projection with respect to any prescribed threshold value for the visual error. This projection can then be processed by various local rendering methods, e.g. color coding of data or isosurface extraction. Especially for color coding purposes modern texture capabilities are used to directly render higher polynomial data by superposition of polynomial basis function textures and final color look-up tables. Numerical experiments from CFD clearly demonstrate the applicability and efficiency of our approach.}, author = {Haasdonk, Bernard and Ohlberger, Mario and Rumpf, Martin and Schmidt, Alfred and Siebert, Kunibert G.}, doi = {10.1007/s00607-003-1476-2}, journal = {Computing}, number = 3, owner = {kohlsk}, 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
  @inproceedings{bahlmann2002online, 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, B. and Burkhardt, H.}, booktitle = {Proc. of the 8th International Workshop on Frontiers in Handwriting Recognition}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Bahlmann2002_www_IWFHR2002.pdf:PDF}, 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
  @inproceedings{haasdonk2002tangent, 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, B. and Keysers, D.}, booktitle = {Proceedings of the 16th International Conference on Pattern Recognition}, 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. Kr�ner, 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, pp. 459--484, 2001.
  - BibTeX
  @article{haasdonk2001convergence, author = {Haasdonk, B. and Kr�ner, 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
  @techreport{haasdonk2001hpmultiresolution, author = {Haasdonk, B. and Ohlberger, M. and Rumpf, M. and Schmidt, A. and Siebert, K.-G.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Haasdonk2001c_www_h_p_vis_grape_preprint.pdf:PDF}, 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, pp. 459--484, 2001.
  - BibTeX
  - Link
  @article{haasdonk2001convergence, author = {Haasdonk, B. and Kr{\"o}ner, D. and Rohde, C.}, coden = {NUMMA7}, doi = {10.1007/s211-001-8011-x}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Haasdonk2001a_www_preprint_StgLxF_convergence.pdf:PDF}, fjournal = {Numerische Mathematik}, 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 }
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
  @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, 28, 1999.
  - 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. B. Haasdonk, “Konvergenz eines Staggered Lax-Friedrichs Verfahrens auf unstrukturierten 2D Gittern,” 1999.
  - BibTeX
  @mastersthesis{haasdonk1999konvergenz, author = {Haasdonk, B.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Haasdonk1999_www_Diplomarbeit_Uni_Freiburg.pdf:PDF}, owner = {haasdonk}, school = {Universit�t Freiburg, Abteilung f�r Angewandte Mathematik}, title = {Konvergenz eines Staggered {L}ax-{F}riedrichs {V}erfahrens auf unstrukturierten 2D {G}ittern}, year = 1999 }

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Bernard Haasdonk

Head of Group Dean of Studies (B.Sc./M.Sc. Mathematik)

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Dean of Studies (B.Sc./M.Sc. Mathematik)