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Wittwar, Dominik

Dominik Wittwar

Dr.

Research assistant
Institute of Applied Analysis and Numerical Simulation
Working Group Numerical Mathematics

Contact

+49 711 685 62013
+49 711 685 65507
Email

Pfaffenwaldring 57
70569 Stuttgart
Germany
Room: 7.116

Publications

Publlications:

2019
1. M. Köppel et al., “Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario,” Comput. Geosci., vol. 2, no. 23, Art. no. 23, 2019, doi: https://doi.org/10.1007/s10596-018-9785-x.
  - BibTeX
  - Link
  BibTeX
  @article{koppel2017comparison, abstract = {A variety of methods is available to quantify uncertainties arising within the modeling of flow and transport in carbon dioxide storage, but there is a lack of thorough comparisons. Usually, raw data from such storage sites can hardly be described by theoretical statistical distributions since only very limited data is available. Hence, exact information on distribution shapes for all uncertain parameters is very rare in realistic applications. We discuss and compare four different methods tested for data-driven uncertainty quantification based on a benchmark scenario of carbon dioxide storage. In the benchmark, for which we provide data and code, carbon dioxide is injected into a saline aquifer modeled by the nonlinear capillarity-free fractional flow formulation for two incompressible fluid phases, namely carbon dioxide and brine. To cover different aspects of uncertainty quantification, we incorporate various sources of uncertainty such as uncertainty of boundary conditions, of conceptual model definitions and of material properties. We consider recent versions of the following non-intrusive and intrusive uncertainty quantification methods: arbitary polynomial chaos, spatially adaptive sparse grids, kernel-based greedy interpolation and hybrid stochastic Galerkin. The performance of each approach is demonstrated assessing expectation value and standard deviation of the carbon dioxide saturation against a reference statistic based on Monte Carlo sampling. We compare the convergence of all methods reporting on accuracy with respect to the number of model runs and resolution. Finally we offer suggestions about the methods� advantages and disadvantages that can guide the modeler for uncertainty quantification in carbon dioxide storage and beyond.}, author = {K\{"o}ppel, M. and Franzelin, F. and Kr\{"o}ker, I. and Oladyshkin, S. and Santin, G. and Wittwar, D. and Barth, A. and Haasdonk, B. and Nowak, W. and Pfl\{"u}ger, D. and Rohde, C.}, doi = {https://doi.org/10.1007/s10596-018-9785-x}, journal = {Comput. Geosci.}, number = 23, owner = {santinge}, pages = {339-354}, publisher = {Springer International Publishing}, title = {Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario}, url = {https://doi.org/10.1007/s10596-018-9785-x}, volume = 2, year = 2019 }
  Link
  https://doi.org/10.1007/s10596-018-9785-x
2018
1. D. Wittwar and B. Haasdonk, “Greedy Algorithms for Matrix-Valued Kernels,” University of Stuttgart, 2018. [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1773
  - BibTeX
  - Link
  BibTeX
  @techreport{wittwar2018greedy, abstract = {We are interested in approximating vector-valued functions on a compact set $\Omega\subset \mathbb R^d$. We consider reproducing kernel Hilbert spaces of $\mathbb R^m$-valued functions which each admit a unique matrix-valued reproducing kernel $k$. These spaces seem promising, when modelling correlations between the target function components. The approximation of a function is a linear combination of matrix-valued kernel evaluations multiplied with coefficient vectors. To guarantee a fast evaluation of the approximant the expansion size, i.e. the number of centers $n$ is desired to be small. We thus present three different greedy algorithms by which a suitable set of centers is chosen in an incremental fashion: First, the $P$-Greedy which requires no function evaluations, second and third, the $f$-Greedy and $f/P$-Greedy which require function evaluations but produce centers tailored to the target function. The efficiency of the approaches is investigated on some data from an artificial model.}, author = {Wittwar, Dominik and Haasdonk, Bernard}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/WH18_www_greedy_matrix_valued.pdf:PDF}, institution = {University of Stuttgart}, owner = {santinge}, title = {Greedy Algorithms for Matrix-Valued Kernels}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1773}, year = 2018 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1773
2017
1. D. Wittwar, A. Schmidt, and B. Haasdonk, “Reduced Basis Approximation for the Discrete-time Parametric Algebraic Riccati Equation,” University of Stuttgart, 2017.
  - BibTeX
  BibTeX
  @techreport{wittwar2017reduced, author = {Wittwar, D. and Schmidt, A. and Haasdonk, B.}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/WSH17_www.pdf:PDF}, institution = {University of Stuttgart}, owner = {schmidta}, title = {Reduced Basis Approximation for the Discrete-time Parametric Algebraic {R}iccati Equation}, year = 2017 }
2014
1. D. Wittwar, “Empirische Interpolation and Anwendung zur Numerischen Integration.” 2014.
  - BibTeX
  BibTeX
  @misc{wittwar2014empirische, author = {Wittwar, D.}, note = {Bachelor's thesis, University of Stuttgart}, owner = {maieril}, title = {Empirische Interpolation and Anwendung zur Numerischen Integration}, year = 2014 }

Teaching

SS 2020: Höhere Mathematik 2
WS 2019: Höhere Mathematik 1
WS 2018: Höhere Mathematik 3
WS 2017: Partielle Differentialgleichungen (Modellierung, Analysis, Simulation)
SS 2017: Numerische Mathematik 2
WS 2016: Höhere Mathematik 3

Vita

since 06.2016	reasearch associate at the University of Stuttgart
November 18, 2021	Ph.D. at the Institute of Applied Analysis and Numerical Simulation, University of Stuttgart
2014-2016	Master studies in mathematics at the Univeristy of Stuttgart
2011-2014	Bachelor studies in mathematics at the University of Stuttgart

Dominik Wittwar

Contact

Publications

2019

BibTeX

Link

2018

BibTeX

Link

2017

BibTeX

2014

BibTeX

Teaching

Vita

Audience

Formalities

Services

Organization

Dominik Wittwar

Contact

Publications

2019

BibTeX

Link

2018

BibTeX

Link

2017

BibTeX

2014

BibTeX

Teaching

Vita

Here you can reach us

Audience

Formalities

Services

Organization