Prof. Dr. Mario Bebendorf

E-mail: bebendorf(at)
Phone: +49 228 73 3144
Room: 4.006
Location: Wegelerstr. 6
Institute: Institute for Numerical Simulation
Research Areas: Research Area B
Research Area J

Academic Career


Diploma in Mathematics, Kaiserslautern University


Dr. rer. nat., Saarland University


Postdoc, Max-Planck-Institute MiS, Leipzig University


Junior Professor (W1), Leipzig University


Replacement professorship, Bonn


Professor (W2), Bonn

Research Profile

Efficient numerical treatment of non-local operators;
preconditioning; efficient approximation of multivariate functions

Research Projects and Activities

Project leader of a project ''Multiscale problems and hierarchical matrices'' in the Collaborative Research Center SFB 611; DFG individual grant ''Tensorwertige Approximation mit Anwendungen in der Akustik und Elektrodynamik''; Cooperation contract with ABB, Switzerland.

Contribution to Research Areas

Research Area B
One of the numerical challenges in micromagnetics is the efficient treatment of the stray field energy. The evaluation involves non-local convolution operators, which after discretization lead to fully populated large scale matrices. For some geometries the computation can be accelerated via the fast Fourier transform. However, the formation of certain patterns strongly depends on the geometry. In order to be able to observe such effects and validate the theoretical findings via numerical simulation, an efficient technique is required that is able to treat general geometries. During the last years, our aim has been to apply the adaptive cross approximation method which constructs approximation in the set of hierarchical matrices with logarithmic-linear complexity. The results of this work have led to an improved approximation technique [1]. Based on this technique we have developed in cooperation with S
"oren Bartels and Felix Otto a simulation tool for the efficient computation of the magnetic field for general settings.
Research Area J
We extended the so-called adaptive cross approximation for the efficient treatment of systems of linear equation to multivariate functions and studied their convergence properties for a wide class of kernel functions [2]. Together with Stefan M
"uller we proved the independence of weighted Poincar
'e inequalities from high-contrast coefficients in rather general situations in [3].

Selected Publications

MathSciNet Publication List (external link)



Feoder Lynen research fellowship (Alexander von Humbold foundation)

Selected Invited Lectures


UKBIM6, Durham, UK


Preconditioning 2007, Toulouse University, France



Professorship (W2), Kassel University


Professorship (W3), TU Hamburg-Harburg

Supervised Theses

  • Bachelor theses: 3
  • Master theses: 1, currently 1
  • Diplom theses: 8, currently 3
  • PhD theses: 5, currently 4
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