| Available projects |
Postdoctoral:
- upon request
Doctoral degree:
- upon request
Master thesis:
- upon request
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| :: General Research Interests
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My research interests are in applied and computational mathematics
driven by applications. I find it highly motivating to deal with a
real life problem, starting with the appropriate modeling of the
situation using physics, then performing a mathematical analysis of
the model and finally implementing an algorithm on a high speed
computer to obtain the results needed in practice. To exploit
computational power to its limit this blend of physical insight,
mathematical analysis and computer science is essential. I also enjoy
to work together with other people, which is natural in applications.
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| :: Current Research Activities (preprints) |
Domain Decomposition: Optimized Schwarz and Schur methods which
work with new transmission conditions and have greatly enhanced
performance. We are working on hyperbolic, parabolic and elliptic
problems of Helmholtz and convection diffusion type. The best
optimized Schwarz preconditioner so far with overlap h has an
asymptotic condition number of O(h^(-1/5)).
Waveform Relaxation: These methods are very slow in their
classical form for circuit simulation, but with new coupling
conditions they become very effective while staying completely
parallel. The reduction in iteration counts for an RC type circuit
is a factor of 3, without additional cost per iteration.
Preconditioners: We are working on a new ILU preconditioner
based on the analytic factorization of the underlying partial
differential operator. While classical ILU preconditioners give
a condition number O(h^(-2)) for a discretized Poisson problem, the new
AILU gives O(h^(-2/3)).
Geometric Integration: Geometric integration methods have the
capability to preserve some of the underying physical properties of
the solution in the numerical approximation. My main interests are in
exact numerical methods for blow up problems and symplectic methods
for Hamiltonian problems.
Hyperbolic Conservation Laws: We are studying the asymptotic
stability and travelling wave solutions of a model with local and
non-local terms.
Krylov Subspace Methods: I am interested in the analysis of
Krylov methods with flexible preconditioning. In particular I have
shown that FGMRES preconditioned by GMRES can not converge with less
matrix vector multiplications than GMRES without preconditioner.
Mathematical Biology: This was my first field of research and I
am still active in it. We develop on the one hand models of population
growth and on the other hand analyze numerical methods for them as dynamical
systems.
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| :: Finished Research Projects (preprints) |
Semiconductor Process Simulation: I have been involved in the
implementation of an object oriented process simulator. New
differential operators can be added as building blocks to put together
new PDEs which are solved with the same code.
Gauss Quadrature Rules: It is intriguing that the computation of
Gauss quadrature rules for a given measure is prone with
instabilities. We investigated a stable discretization procedure due to
Gautschi and stabilization procedures of the underlying Lanczos
process.
Interference in Cellular Phone Systems: Cellular phones are more
and more common and companies need to fight for bandwidth. Naturally
the problem arises how to optimally use bandwidth. This leads to an
NP-hard problem which we solved approximately using linear algebra
techniques.
Cryptography: This was my master thesis at ETH, a provably
secure transmission over an insecure channel without having to resort
to an NP-hard problem.
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