Prof. Dr. Markus Bachmayr

I have moved to Hausdorff Center for Mathematics & Institute for Numerical Simulation, University of Bonn.



Publications

Preprints

M. Bachmayr, A. Cohen, and W. Dahmen, Parametric PDEs: Sparse or low-rank approximations?, arXiv:1607.04444.
M. Bachmayr, A. Cohen, and G. Migliorati, Representations of Gaussian random fields and approximation of elliptic PDEs with lognormal coefficients, arXiv:1603.05559.

Journal Publications

M. Bachmayr, A. Cohen, R. DeVore, and G. Migliorati, Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients, accepted for publication in ESAIM: M2AN (preprint: arXiv:1509.07050).
M. Bachmayr, A. Cohen, and G. Migliorati, Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients, accepted for publication in ESAIM: M2AN (preprint: arXiv:1509.07045).
M. Bachmayr and A. Cohen, Kolmogorov widths and low-rank approximations of parametric elliptic PDEs, Mathematics of Computation, DOI 10.1090/mcom/3132, 2016.
M. Bachmayr, R. Schneider, and A. Uschmajew, Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations, Foundations of Computational Mathematics, DOI 10.1007/s10208-016-9317-9.
M. Bachmayr and R. Schneider, Iterative methods based on soft thresholding of hierarchical tensors, Foundations of Computational Mathematics, DOI 10.1007/s10208-016-9314-z.
M. Bachmayr and W. Dahmen, Adaptive low-rank methods for problems on Sobolev spaces with error control in L2, ESAIM: M2AN, 50(4), pp 1107-1136, 2016.
M. Bachmayr and W. Dahmen, Adaptive low-rank methods: Problems on Sobolev spaces, SIAM Journal on Numerical Analysis 54(2), pp 744-796.
M. Bachmayr and 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, and L. Grasedyck, Approximation of high-dimensional rank one tensors, Constructive Approximation, 39(2), pp 385-395, 2014.
M. Bachmayr, H. Chen, and 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 and M. Burger, Iterative total variation schemes for nonlinear inverse problems, Inverse Problems 25 105004, 2009.

Further Publications

M. Bachmayr, Kolmogorov widths and low-rank approximations of parametric elliptic PDEs, to appear 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.
PhD thesis: Adaptive low-rank wavelet methods and applications to two-electron Schrödinger equations, RWTH Aachen, 2012. Advisors: W. Dahmen, K. Veroy-Grepl
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.
Master thesis: Iterative total variation methods for nonlinear inverse problems, Johannes Kepler Universität Linz, 2007. Advisor: M. Burger

Awards

John Todd Award 2013 for excellent achievements in Numerical Analysis, awarded by Oberwolfach Foundation and MFO
Borchers Plakette, RWTH Aachen
Erwin Wenzl Preis 2007, awarded for Master thesis

Teaching

Previous courses at RWTH Aachen

  • summer '16: Inverse Problems
  • summer '14: Numerische Mathematik für Maschinenbauer
  • summer '13: Numerische Analysis II
  • winter '12/'13:Numerische Analysis I
  • summer '12:Numerische Mathematik für Maschinenbauer
  • winter '11/'12:Adaptive Lösungskonzepte