TU Berlin

Numerische MathematikResearch

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Research Areas

Numerical Mathematics
Numerical solution of differential-algebraic equations
Numerical methods for linear and nonlinear systems
Numerical solution of optimal control problems
Numerical solution of partial differential equations
Numerical methods for linear and nonlinear eigenvalue problems

Construction of preconditioners for linear systems
Numerical compuation of smooth factorizations of matrix values functions
Parallelisation of numerical algorithms
Numerical methods for regularization and stabilzation of dynmical systems and control systems
Numerical computation of structured normal forms
Numerical computation of of Lyapunov and Sacker-Sell spektra
Software deelopment in numerical methods
Control theory
Singular control problems
Optimal pole placement and stabilization methods
Error analysis and software development in numerical control algorithms

Open and closed loop control of descriptor systems

Optimal control
Matrix theory
Theory of nonnegative matrices and their generalizations

Nonlinear eigenvalue problems
Normal forms
Matrix polynomials

Projects

Third party funding: 2000-today
Network for Development and Evaluation of Numerically Reliable Software in Control Engineering and its Implementation in Production Technologies (NICONET), Brite/EuRam III RTD Thematic Network, funded by European  Union, 1. January 98 -31. December 2001, with NAG (Numerical Algorithms Group) (S. Hammarling), DLR Oberpfaffenhoven (A. Varga and G. Grübel), KU Leuven (S. Van Huffel), UC Louvain (P. Van Dooren), TU Eindhoven (A. van den Boom und A. Stoorvogel) TU Delft (M. Verhaegen), and several industrial partners
Analysis and numerics of under and overdetermined nonlinear differential-algebraic equations, DFG-research project, with P. Kunkel, Univ. Oldenburg, 1. September 1998-31. August 2000.
Numerical simulation of train traffic in large networks
BMBF-research project, with companies  TLC and DB Netz (Frankfurt) 1. January 2001-31.December 2003
Numerical methods of robust control,
DFG-research project with P. Benner and A. Bunse-Gerstner, Univ. Bremen and A. Varga, DLR, Oberpfaffenhoven, 1. October 2000-30. September 2003
Kalibation methods for hypbrid parallel kinemtaic robots,
DFG-project in priority program  Fertigungsmaschinen mit Parallelkinematiken with H. Tönshoff, Hannover, 1. October 2000-30. September 2001
Analysis and numerics of under and overdetermined nonlinear differential-algebraic equations, DFG-research project, with P. Kunkel, Univ. Oldenburg, 1. September 2000-31. August 2002.
Analysis and modelling of drop size distriutions in stirred liquid/liquid systems, projekt  in DFG research traning group  827, transport phenomena on moving phase boundaries,  with M. Kraume TU Berlin, 1. October 2002-30. September 2005
Con founder and vice chair  (2002-2008), chair (2008- ) of DFG Research center MATHEON, Mathematics for key technologies, 01.June 2002--30 May.2014

Projects 2002-2006:

C4: Numerical solution of large nonlinear eigenvalue problems,
with C. Mehl,
D1: Model reduction for large-scale systems in control and
circuit simulation, with P. Benner and  F. Tröltzsch,
D2: Solution of large unstructured linear systems in circuit
simulation, with M. Bollhofer,
D5: Structure analysis for simulation and control problems of
differential algebraic equations with R. März,

Projects 2006-2010:

A9: Simulation and control of positive descriptor systems,
with R. Nabben
C4: Numerical solution of large nonlinear eigenvalue problems,
with C. Mehl
C22: Adaptive solution of parametric eigenvalue problems for
partial differential equations,
with C. Carstensen und C. Mehl
D1: Simulation and control of switched systems of
differential-algebraic equations
D2: Passivation of linear time invariant systems arising in
circuit simulation and electric field computation,
with C. Mehl,
D18: Sparse representation of solutions of differential  equations,
with M. Pfetsch and H. Yserentant.

Projects 2010-2014:

D2: Passivation of linear time invariant systems arising in circuit simulation and electric field computation, (with T. Reis until 30. September 2011)
C22: Adaptive solution of parametric eigenvalue problems for partial differential equations
with C. Carstensen
C29: Numerical methods for large-scale parameter-dependent systems,
with J. Liesen, R. Nabben, (T. Stykel until 30.09.2011) and C. Mehl (from 01.10.2011)
Numerical solution of quadratic operator eigenvalue problems from continuum mechanics DFG- research project with T. Apel, TU Chemnitz, 1. January 2002- 31. January 2006
System reduction and optimal  control in the control of flows.
Project in Collaborative Research Center SFB 557, with F. Tröltzsch, 1. July 2004--30. June 2010.
Numerical algorithms for generalized eigenvalue problem of even structure with applications to
robust control of  descriptor systems.
DFG-research project with P. Benner, TU Chemnitz, 1.January 2006--30. April 2010
Computation of density distribution functions for stochastically excited mechanical systems via the solution of Fokker-Planck equations
DFG-research project with Utz von Wagner, Inst. f. Mechanik, TU Berlin, 1. April 2008--31. March 2011.
Scalable numerical methods for adiabatic quantum preparation, 
DFG-research project with T. Brandes, Inst. f. theoretische Physik, TU Berlin, 1. September 2010-
Modelling, simulation, and control of drop size distriutions in stirred liquid/liquid systems
DFG-research project with M. Kraume, Fachgebiet für Verfahrenstechnik, TU Berlin and M. Schäfer, Fachgebiet Numerische Berechnungsverfahren im Maschinenbau, TU Darmstadt, 1. January 2009-
Analysis, numerical solution and control of delay-differential-algebraic equations, Project A2 in DFG Collaborative Research Center SFB 910, (with T. Stykel until 30. Septmber 2011), 1. January 2011-
ERC Advanced Grant: MODSIMCONMP Modelling, Simulation and Control of Multiphysics Systems, 1. April 2011-31. March 2016
Numerous industrial cooperations with
Bosch-Rexroth, Lohr,
CST GmbH, Darmstadt,
DaimlerChrysler Research Esslingen,
Deutsche Bahn Systems, Frankfurt,
NEC Europe, St. Augustin,
SFE GmbH Berlin,

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