Prof. Dr. Markus Bachmayr


Research Interests

  • Nonlinear approximation and adaptive methods
  • High-dimensional partial differential equations
  • Uncertainty quantification and inverse problems
  • Numerical methods in quantum chemistry

Master theses topics related to these research areas are available. Please contact Prof. Bachmayr directly for further details.

Third-party funding


Teaching

summer term 19

winter term 18/19


Publications

Preprints

M. Bachmayr and V. K. Nguyen, Identifiability of diffusion coefficients for source terms of non-uniform sign, arXiv:1809.05178.
M. Bachmayr and V. Kazeev, Stability of low-rank tensor representations and structured multilevel preconditioning for elliptic PDEs, arXiv:1802.09062

Journal articles

B. Arras, M. Bachmayr, and A. Cohen, Sequential sampling for optimal weighted least squares approximations in hierarchical spaces, arXiv:1805.10801, to appear in SIAM Journal on Mathematics of Data Science.
M. Bachmayr, A. Cohen, and W. Dahmen, Parametric PDEs: Sparse or low-rank approximations? IMA Journal of Numerical Analysis, 38(4), pp 1661-1708, 2018.
M. Bachmayr, A. Cohen, and 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, and 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, and 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, and 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 and R. Schneider, Iterative methods based on soft thresholding of hierarchical tensors, Found. Comput. Math., 17(4), pp 1037-1083, 2017.
M. Bachmayr and A. Cohen, Kolmogorov widths and low-rank approximations of parametric elliptic PDEs, Mathematics of Computation, 86, pp 701-724, 2017.
M. Bachmayr, R. Schneider, and 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.
M. Bachmayr and W. Dahmen, Adaptive low-rank methods: Problems on Sobolev spaces, SIAM J. Numer. Anal., 54(2), pp 744-796, 2016.
M. Bachmayr and 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 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, 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.

Theses

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

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