Prof. Dr. Markus Bachmayr


Forschungsschwerpunkte

  • Nichtlineare Approximation und adaptive Verfahren
  • hochdimensionale partielle Differentialgleichungen
  • Uncertainty Quantification und inverse Probleme
  • Numerische Methoden in der Quantenchemie

Masterarbeiten im Umfeld dieser Forschungsthemen können jederzeit vergeben werden. Wenn Sie daran interessiert sind, setzen Sie sich bitte direkt mit Prof. Bachmayr für einen Besprechungstermin in Verbindung.

Drittmittel


Lehre

Wintersemester 19/20

Sommersemester 19

Wintersemester 18/19


Publikationen

Preprints

M. Bachmayr, I. G. Graham, V. K. Nguyen und R. Scheichl, Unified analysis of periodization-based sampling methods for Matérn covariances, arXiv:1905.13522.

Referierte Zeitschriftenartikel

M. Bachmayr und V. Kazeev, Stability of low-rank tensor representations and structured multilevel preconditioning for elliptic PDEs, arXiv:1802.09062, erscheint in Foundations of Computational Mathematics.
M. Bachmayr und W. Dahmen, Adaptive Low-Rank Approximations for Operator Equations: Accuracy Control and Computational Complexity, arXiv:1910.07052 (Übersichtsartikel), erscheint in Contemporary Mathematics.
M. Bachmayr und V. K. Nguyen, Identifiability of diffusion coefficients for source terms of non-uniform sign, Inverse Problems & Imaging, 13 (5), pp 1007-1021, 2019.
B. Arras, M. Bachmayr, und A. Cohen, Sequential sampling for optimal weighted least squares approximations in hierarchical spaces, SIAM Journal on Mathematics of Data Science, 1(1), pp 189-207, 2019.
M. Bachmayr, A. Cohen, und W. Dahmen, Parametric PDEs: Sparse or low-rank approximations? IMA Journal of Numerical Analysis, 38(4), pp 1661-1708, 2018.
M. Bachmayr, A. Cohen, und G. Migliorati, Representations of Gaussian random fields and approximation of elliptic PDEs with lognormal coefficients, J. Fourier Anal. Appl., 24(3), pp 621-649, 2018.
M. Bachmayr, A. Cohen, D. Dũng, und Ch. Schwab, Fully discrete approximation of parametric and stochastic elliptic PDEs, SIAM J. Numer. Anal., 55, 2151-2186, 2017.
M. Bachmayr, A. Cohen, R. DeVore, und G. Migliorati, Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients, ESAIM Math. Model. Numer. Anal., 51(1), pp 341-363, 2017.
M. Bachmayr, A. Cohen, und G. Migliorati, Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients, ESAIM Math. Model. Numer. Anal., 51(1), pp 321-339, 2017.
M. Bachmayr und R. Schneider, Iterative methods based on soft thresholding of hierarchical tensors, Found. Comput. Math., 17(4), pp 1037-1083, 2017.
M. Bachmayr und A. Cohen, Kolmogorov widths and low-rank approximations of parametric elliptic PDEs, Mathematics of Computation, 86, pp 701-724, 2017.
M. Bachmayr, R. Schneider, und A. Uschmajew, Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations, Found. Comput. Math., 16(6), pp 1423-1472, 2016. (Übersichtsartikel)
M. Bachmayr und W. Dahmen, Adaptive low-rank methods: Problems on Sobolev spaces, SIAM J. Numer. Anal., 54(2), pp 744-796, 2016.
M. Bachmayr und W. Dahmen, Adaptive low-rank methods for problems on Sobolev spaces with error control in L2, ESAIM Math. Model. Numer. Anal., 50(4), pp 1107-1136, 2016.
M. Bachmayr und W. Dahmen, Adaptive near-optimal rank tensor approximation for high-dimensional operator equations, Foundations of Computational Mathematics, 15(4), pp 839-898, 2015.
M. Bachmayr, W. Dahmen, R. DeVore, und L. Grasedyck, Approximation of high-dimensional rank one tensors, Constructive Approximation, 39(2), pp 385-395, 2014.
M. Bachmayr, H. Chen, und R. Schneider, Error estimates for Hermite and even-tempered Gaussian approximations in quantum chemistry, Numerische Mathematik, 128(1), pp 137-156, 2014.
M. Bachmayr, Integration of products of Gaussians and wavelets with applications to electronic structure calculations, SIAM J. Numer. Anal., 51(5), pp 2491-2513, 2013.
M. Bachmayr, Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation, ESAIM: M2AN 46(6), pp 1337-1362, 2012.
M. Bachmayr und M. Burger, Iterative total variation schemes for nonlinear inverse problems, Inverse Problems 25 105004, 2009.

Weitere Publikationen

M. Bachmayr, Space-parameter-adaptive approximation of affine-parametric elliptic PDEs, in Oberwolfach Report 17/2017, Mathematisches Forschungsinstitut Oberwolfach.
M. Bachmayr, Kolmogorov widths and low-rank approximations of parametric elliptic PDEs, in Oberwolfach Report 2/2015, Mathematisches Forschungsinstitut Oberwolfach.
M. Bachmayr, Adaptivity and preconditioning for high-dimensional elliptic partial differential equations, in Oberwolfach Report 24/2014, Mathematisches Forschungsinstitut Oberwolfach.
M. Bachmayr, Adaptive near-optimal rank tensor approximation for high-dimensional operator equations, in Oberwolfach Report 39/2013, Mathematisches Forschungsinstitut Oberwolfach.
M. Bachmayr, Hyperbolic wavelet discretization of the electronic Schrödinger equation: Explicit correlation and separable approximation of potentials, in Oberwolfach Report 33/2010, Mathematisches Forschunginstitut Oberwolfach.

Abschlussarbeiten

Dissertation: Adaptive low-rank wavelet methods and applications to two-electron Schrödinger equations, RWTH Aachen, 2012.
Masterarbeit: Iterative total variation methods for nonlinear inverse problems, Johannes Kepler Universität Linz, 2007.

Auszeichnungen

John Todd Award 2013 für herausragende Leistungen in Numerischer Analysis, Oberwolfach Foundation und MFO
Borchers Plakette, RWTH Aachen
Erwin Wenzl Preis 2007, Kategorie Masterarbeit