Research Group of Prof. Dr. Markus Bachmayr

Mr. Bachmayr has left the institute. This page is no longer maintained.

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Research Topics

  • Nonlinear approximation and adaptive methods
  • High-dimensional partial differential equations
  • Applications in quantum chemistry and in uncertainty quantification

News

  • New preprint Stability of low-rank tensor representations and structured multilevel preconditioning for elliptic PDEs (with V. Kazeev)

Research seminar series Mathematics of Computation

Upcoming Conferences

Teaching

Summer semester 2018

Winter semester 2017/18

Winter semester 2016/17

See teaching activities of the whole group.

Current Research Projects

Publications

Preprints

  1. Stability of low-rank tensor representations and structured multilevel preconditioning for elliptic PDEs. M. Bachmayr and V. Kazeev. arXiv:1802.09062, 2018. Also available as INS Preprint No. 1802. BibTeX arXiv

Journal Papers

  1. Kolmogorov widths and low-rank approximations of parametric elliptic PDEs. M. Bachmayr and A. Cohen. Mathematics of Computation, 86:701–724, 2017. BibTeX DOI arXiv
  2. Parametric PDEs: Sparse or low-rank approximations? M. Bachmayr, A. Cohen, and W. Dahmen. IMA Journal of Numerical Analysis, 2017. To appear. BibTeX DOI arXiv
  3. Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients. M. Bachmayr, A. Cohen, R. DeVore, and G. Migliorati. ESAIM Math. Model. Numer. Anal., 51(1):341–363, 2017. BibTeX DOI arXiv
  4. Representations of Gaussian random fields and approximation of elliptic PDEs with lognormal coefficients. M. Bachmayr, A. Cohen, and G. Migliorati. J. Fourier Anal. Appl., 2017. To appear. BibTeX DOI arXiv
  5. Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients. M. Bachmayr, A. Cohen, and G. Migliorati. ESAIM Math. Model. Numer. Anal., 51(1):321–339, 2017. BibTeX DOI arXiv
  6. Fully discrete approximation of parametric and stochastic elliptic PDEs. M. Bachmayr, Albert, Cohen, D. Dũng, and C. Schwab. SIAM J. Numer. Anal., 55:2151–2186, 2017. BibTeX DOI arXiv
  7. Iterative methods based on soft thresholding of hierarchical tensors. M. Bachmayr and R. Schneider. Found. Comput. Math., 17(4):1037–1083, 2017. BibTeX DOI
  8. Adaptive low-rank methods for problems on Sobolev spaces with error control in L2L_2. M. Bachmayr and W. Dahmen. ESAIM Math. Model. Numer. Anal., 50(4):1107–1136, 2016. BibTeX DOI
  9. Adaptive low-rank methods: problems on Sobolev spaces. M. Bachmayr and W. Dahmen. SIAM J. Numer. Anal., 54(2):744–796, 2016. BibTeX DOI
  10. Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations. M. Bachmayr, R. Schneider, and A. Uschmajew. Found. Comput. Math., 16(6):1423–1472, 2016. BibTeX DOI
  11. Adaptive near-optimal rank tensor approximation for high-dimensional operator equations. M. Bachmayr and W. Dahmen. Found. Comput. Math., 15(4):839–898, 2015. BibTeX DOI
  12. Error estimates for Hermite and even-tempered Gaussian approximations in quantum chemistry. M. Bachmayr, H. Chen, and R. Schneider. Numer. Math., 128(1):137–165, 2014. BibTeX DOI
  13. Approximation of high-dimensional rank one tensors. M. Bachmayr, W. Dahmen, R. DeVore, and L. Grasedyck. Constr. Approx., 39(2):385–395, 2014. BibTeX DOI
  14. Integration of products of Gaussians and wavelets with applications to electronic structure calculations. M. Bachmayr. SIAM J. Numer. Anal., 51(5):2491–2513, 2013. BibTeX DOI
  15. Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation. M. Bachmayr. ESAIM Math. Model. Numer. Anal., 46(6):1337–1362, 2012. BibTeX DOI
  16. Iterative total variation schemes for nonlinear inverse problems. M. Bachmayr and M. Burger. Inverse Problems, 25(10):105004, 26, 2009. BibTeX DOI

Thesis

  1. Adaptive Low-Rank Wavelet Methods and Applications to Two-Electron Schrödinger Equations. M. Bachmayr. PhD thesis, RWTH Aachen, 2012. BibTeX
  2. Iterative total variation methods for nonlinear inverse problems. M. Bachmayr. Master's thesis, Johannes Kepler Universität Linz, 2007. BibTeX

Other Reports

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