Martin J. Gander
Section de Mathématiques
Université de Genève
Rue du Conseil-Général 9, CP 64
1211 Genève 4, Suisse
martin.gander(at)   Fax: +41 22 379 11 76

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- Analyse numérique
- Applied Mathematics
Ascona 2013

Available projects
- upon request
Doctoral degree:
- upon request
Master thesis:
- upon request

DDM on the Web
I was the chair of the international scientific committee on Domain Decomposition methods from 2013-2020

:: General Research Interests (preprints)
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.
:: 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.
:: 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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