Team Leader NLMA

Prof. Dr. Peter Benner
Prof. Dr. Peter Benner
Phone: +49 391 6110 450
Fax: +49 391 6110 453
Room: S2.15

Team members

Dr. Pawan Goyal
Dr. Pawan Goyal
Phone: +49 391 6110 386
Room: S3.09
Carolin Penke, M.Sc.
Carolin Penke, M.Sc.
Phone: +49 391 6110 806
Room: S3.09
Roman Weinhandl
Phone: +49 391 6110 472
Room: S2.14
M.Sc. Kirandeep Kour
M.Sc. Kirandeep Kour
Phone: +49 391 6110 469
Room: S2.09
Links: Linkedin
Dr. Jens Saak
Dr. Jens Saak
Team leader

Phone: +49 391 6110 216
Room: S2.20
Dr. Yue Qiu
Dr. Yue Qiu
Phone: +49 391 6110 395
Room: S3.13
Dipl.-Math. Martin Köhler
Dipl.-Math. Martin Köhler
Phone: +49 391 6110 445
Fax: +49 391 6110 453
Room: S3.10

Numerical Linear and Multilinear Algebra

Numerical Linear and Multilinear Algebra

We study numerical methods for linear and nonlinear eigenvalue problems. This includes the development and analysis of new algorithms, (backward) error analysis, and the derivation of the associated (relative) perturbation theory. Special attention is given to linear, generalized, and polynomial eigenproblems with spectral symmetries. Special cases include:
  • linear eigenproblems for Hamiltonian and symplectic matrices,
  • generalized eigenproblems for skew-Hamiltonian/Hamiltonian, even, and positive definite matrix pencils,
  • as well as even, gyroscopic, and hyperbolic polynomial eigenvalue problems.
Such problems often arise in systems, control and stability theory, FE analysis of corner singularities, discrete approximations to the Schrödinger equation such as the Hartree-Fock and Bethe-Salpeter equations, and many other areas. Another important class of structured eigenproblems investigated by the NLMA team is related to rank-structured matrices and matrix pairs. This includes H- and H2-matrices resulting from FEM and BEM discretizations of PDE eigenvalue problems, but also matricizations of tensor equations in electronic structure calculation.    

Moreover, we investigate the solution of special linear systems of equations arising in PDE control and model reduction algorithms. This includes in particular
  • recycling techniques for Krylov subspace solvers for systems with multiple-right hand sides and constant (or slowly varying) coefficient matrices,
  • preconditioning techniqes for saddle point problems, and
  • using tensor techniques to solve high-dimensional problems like stochastic Galerkin systems.

Projects

Low-rank Methods for Parameter-dependent Fluid-structure Interaction Discretizations

Partners: Prof. Dr. Thomas Richter (Otto von Guericke University Magdeburg)
Funded by: Deutsche Forschungsgemeinschaft (DFG), DFG-GRK 2297
Contact: Roman Weinhandl, Peter Benner [more]
Partners: Zvonimir Bujanović (U Zagreb), Heike Faßbender (TU Braunschweig), Volker Mehrmann, Matthias Voigt (TU Berlin), Hongguo Xu (U Kansas, Lawrence, KS), Chao Yang (Berkeley Lab, CA)Funded by: MPIContact: Peter Benner

Structured (Hamiltonian, even) eigenvalue problems

Partners: Zvonimir Bujanović (U Zagreb), Heike Faßbender (TU Braunschweig), Volker Mehrmann, Matthias Voigt (TU Berlin), Hongguo Xu (U Kansas, Lawrence, KS), Chao Yang (Berkeley Lab, CA)
Funded by: MPI
Contact: Peter Benner

Partners: MPCDF, Claudia Draxl (HU Berlin), Chao Yang (Berkeley Lab, CA), Heike Faßbender (TU Braunschweig), Boris Khoromskii, Venera Khoromskaia (MPI MIS)Funded by: MPI, MPI MIS and MPCDF Funding period: MPI, MPI MIS (2018-2020) and MPCDF (2017-2020)Contact: Peter Benner, Venera Khoromskaia

Efficient solvers for the Bethe-Salpeter equations

Partners: MPCDF, Claudia Draxl (HU Berlin), Chao Yang (Berkeley Lab, CA), Heike Faßbender (TU Braunschweig), Boris Khoromskii, Venera Khoromskaia (MPI MIS)
Funded by: MPI, MPI MIS and MPCDF
Funding period: MPI, MPI MIS (2018-2020) and MPCDF (2017-2020)
Contact: Peter Benner, Venera Khoromskaia
Partners: Boris Khoromskij (MPI, Leipzig), Venera Khoromskaia (MPI, Leipzig) Funded by: MPI MagdeburgContact: Peter Benner, Cleophas Kweyu

Regularization of the Poisson-Boltzmann Equation by the Range-Separated Tensor Format

Partners: Boris Khoromskij (MPI, Leipzig), Venera Khoromskaia (MPI, Leipzig)
Funded by: MPI Magdeburg
Contact: Peter Benner, Cleophas Kweyu
Partners: Steffen Börm (CAU Kiel), Boris Khoromskii (MPI MIS), Thomas Mach (KU Leuven), Chao Yang (Berkeley Lab, CA), Sergey Dolgov (U Bath, UK)Funded by: MPI, MPI MISContact: Peter Benner, Venera Khoromskaia

Eigenvalue problems with rank structure

Partners: Steffen Börm (CAU Kiel), Boris Khoromskii (MPI MIS), Thomas Mach (KU Leuven), Chao Yang (Berkeley Lab, CA), Sergey Dolgov (U Bath, UK)
Funded by: MPI, MPI MIS
Contact: Peter Benner, Venera Khoromskaia

Partners: Martin Stoll (TU Chemnitz), Sergey Dolgov (U Bath, UK) Funded by: CDS, IMPRSContact: Peter Benner

Tensor techniques for high-dimensional linear systems

Partners: Martin Stoll (TU Chemnitz), Sergey Dolgov (U Bath, UK)
Funded by: CDS, IMPRS
Contact: Peter Benner

Concluded Projects

Partners: Ninoslav Truhar, Suzana Miodragović (J.J. Strossmayer Univerity Osijek)  Funded by: DAAD PPP (Croatia)  Contact: Peter Benner, Xin Liang

Numerical methods of nonlinear eigenvalue problems

Partners: Ninoslav Truhar, Suzana Miodragović (J.J. Strossmayer Univerity Osijek)
Funded by: DAAD PPP (Croatia)
Contact: Peter Benner, Xin Liang

 
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