Profile
Profile

Prof. Dr. Daniel Peterseim

E-mail: peterseim(at)ins.uni-bonn.de
Phone: +49 228 73 2058
Homepage: http://peterseim.ins.uni-bonn.de/people/peterseim.html
Room: 6.002
Location: Computing Center
Institute: Institute for Numerical Simulation
Research Areas: Research Area B
Research Area J
Mathscinet-Number: 848711

Academic Career

2004

Diploma in Mathematics, TU Ilmenau

2007

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

2007 - 2008

Postdoc, University of Zürich, Switzerland

2009

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”,
Principal Investigator, with Dr.-Ing. Markus Kästner, TU Dresden
within DFG Priority Programme 1748 “Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretization Methods, Mechanical and Mathematical Analysis”

Selected Publications

[1] D. Peterseim
Eliminating the pollution effect in Helmholtz problems by local subscale correction
Math. Comp.
2016
DOI: http://dx.doi.org/10.1090/mcom/3156
[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
2015
ISSN: 0045-7825
DOI: 10.1016/j.cma.2015.06.017
[3] Philipp Morgenstern, Daniel Peterseim
Analysis-suitable adaptive T-mesh refinement with linear complexity
Comput. Aided Geom. Design , 34: : 50--66
2015
ISSN: 0167-8396
DOI: 10.1016/j.cagd.2015.02.003
[4] Axel Målqvist, Daniel Peterseim
Computation of eigenvalues by numerical upscaling
Numer. Math. , 130: (2): 337--361
2015
ISSN: 0029-599X
DOI: 10.1007/s00211-014-0665-6
[5] Patrick Henning, Axel M{\ocirca}lqvist, Daniel Peterseim
Two-level discretization techniques for ground state computations of Bose-Einstein condensates
SIAM J. Numer. Anal. , 52: (4): 1525--1550
2014
ISSN: 0036-1429
DOI: 10.1137/130921520
[6] Daniel Peterseim
Composite finite elements for elliptic interface problems
Math. Comp. , 83: (290): 2657--2674
2014
ISSN: 0025-5718
DOI: 10.1090/S0025-5718-2014-02815-9
[7] Axel Målqvist, Daniel Peterseim
Localization of elliptic multiscale problems
Math. Comp. , 83: (290): 2583--2603
2014
ISSN: 0025-5718
DOI: 10.1090/S0025-5718-2014-02868-8
[8] Patrick Henning, Daniel Peterseim
Oversampling for the multiscale finite element method
Multiscale Model. Simul. , 11: (4): 1149--1175
2013
ISSN: 1540-3459
DOI: 10.1137/120900332
[9] Daniel Peterseim, Carsten Carstensen
Finite element network approximation of conductivity in particle composites
Numer. Math. , 124: (1): 73--97
2013
ISSN: 0029-599X
DOI: 10.1007/s00211-012-0509-1
[10] Lehel Banjai, Daniel Peterseim
Parallel multistep methods for linear evolution problems
IMA J. Numer. Anal. , 32: (3): 1217--1240
2012
ISSN: 0272-4979
DOI: 10.1093/imanum/drq040

Publication List

Selected Invited Lectures

2011

Adaptive Computational PDEs, BITS-Pilani Goa Campus, India

2012

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

2014

London Mathematical Society – EPSRC Durham Symposium, Durham, UK

2015

Chinese-German Workshop on Computational Mathematics, Augsburg

2015

28th FEM-Symposium, Chemnitz

2016

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

Offers

2013

Professor (W2), TU Dresden

2015

Professor (W3), University of Magdeburg

2016

Professor (W3), University of Augsburg

2016

Professor (W3), University of Hannover

2016

Professor (W3), TU Dortmund

Supervised Theses

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