Prof. Dr. Daniel Peterseim

E-mail: peterseim(at)
Phone: +49 228 73 2058
Room: 6.002
Location: Wegelerstr. 6
Institute: Institute for Numerical Simulation
Research Areas: Research Area B
Research Area J

Academic Career


Diploma in Mathematics, TU Ilmenau


Dr. sci. nat., University of Zürich, Switzerland

2007 - 2008

Postdoc, University of Zürich, Switzerland


Postdoc, HU Berlin

2009 - 2013

Junior Research Group Leader, DFG Research Center Matheon / HU Berlin

Since 2013

Professor (W3 - 5y), University of Bonn

Research Profile

My research concerns the algorithms that underlie the computer-aided simulation of multiscale processes in engineering and the sciences and, equally important, the mathematics behind them to foresee and assess their performance in practice. Among the target applications are the mechanical analysis of composite and multifunctional materials and transport processes in porous media such as groundwater flow in unsaturated soils. Although mathematical physics provides sound models of partial differential equations that implicitly describe such processes, the complex interplay of effects between the scales often remains intractable analytically. Hence, the understanding of these processes and their control is intrinsically tied to numerical simulation. In many interesting applications, however, computers are not able to resolve all details on all relevant scales, even in the age of exa-scale computing. My research aims to provide numerical techniques that account for the characteristic features on several levels of numerical resolution in a sophisticated (hierarchical, concurrent and adaptive) way so that the reliable and efficient computer-simulation of multiscale problems eventually becomes feasible. I develop and analyse, e.g., methods for the effective representation of complex geometries, robust discretisation techniques, rigorous approaches to numerical homogenisation, algorithms for automatic mesh refinement based on a priori and a posteriori knowledge about the problem, and strategies for efficient parallel computing.

The new techniques for numerical homogenization yield promising results also for eigenvalue problems. This observation has surprising applications, e.g., the computation of ground states of Bose-Einstein condensates. Future research will address this potential in the context of more general classes of non-linear Schrödinger equations and other nonlinear (polynomial) eigenvalue problems, for example the mechanical analysis of damped vibrating structures. Moreover, multiscale methods can be utilized for stabilization for numerical high-frequency wave propagation. Future research aims to transfer such approaches to parameter studies and inverse problems in geophyiscal and medical applications.

Research Projects and Activities

Project “Adaptive isogeometric modeling of propagating strong discontinuities in heterogeneous materials”,
within DFG Priority Programme 1748 “Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretization Methods, Mechanical and Mathematical Analysis”
Principal Investigator, with Dr.-Ing. Markus Kästner, TU Dresden

Selected Publications

[1] Daniel Peterseim
Eliminating the pollution effect in Helmholtz problems by local subscale correction
Math. Comp. , 86: (305): 1005--1036
[2] D. Gallistl, D. Peterseim
Stable multiscale Petrov-Galerkin finite element method for high frequency acoustic scattering
Comput. Methods Appl. Mech. Engrg. , 295: : 1--17
[3] Philipp Morgenstern, Daniel Peterseim
Analysis-suitable adaptive T-mesh refinement with linear complexity
Comput. Aided Geom. Design , 34: : 50--66
[4] Axel Må lqvist, Daniel Peterseim
Computation of eigenvalues by numerical upscaling
Numer. Math. , 130: (2): 337--361
[5] Patrick Henning, Axel Må lqvist, Daniel Peterseim
Two-level discretization techniques for ground state computations of Bose-Einstein condensates
SIAM J. Numer. Anal. , 52: (4): 1525--1550
[6] Daniel Peterseim
Composite finite elements for elliptic interface problems
Math. Comp. , 83: (290): 2657--2674
[7] Axel Må lqvist, Daniel Peterseim
Localization of elliptic multiscale problems
Math. Comp. , 83: (290): 2583--2603
[8] Patrick Henning, Daniel Peterseim
Oversampling for the multiscale finite element method
Multiscale Model. Simul. , 11: (4): 1149--1175
[9] Daniel Peterseim, Carsten Carstensen
Finite element network approximation of conductivity in particle composites
Numer. Math. , 124: (1): 73--97
[10] Lehel Banjai, Daniel Peterseim
Parallel multistep methods for linear evolution problems
IMA J. Numer. Anal. , 32: (3): 1217--1240

Publication List

MathSciNet Publication List (external link)

Selected Invited Lectures


Adaptive Computational PDEs, BITS-Pilani Goa Campus, India


Conference Dissipative Spectral Theory: Operator Theory, PDEs and Numerics, Cardiff School of Mathematics, Wales, UK


London Mathematical Society – EPSRC Durham Symposium, Durham, England, UK


Chinese-German Workshop on Computational Mathematics, Augsburg


28th FEM-Symposium, Chemnitz


The 5th CAM-ICCM Workshop: Multiscale and Large-scale Scientific Computing, Hong Kong



Professor (W2), TU Dresden


Professor (W3), University of Magdeburg


Professor (W3), University of Augsburg


Professor (W3), University of Hannover


Professor (W3), TU Dortmund

Supervised Theses

  • Master theses: 3, currently 3
  • Diplom theses: 5
  • PhD theses currently: 1
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