Utrecht University has strong research groups, active in a wide variety of topics in Scientific Computing, Computer Science, Aplied Analysis, Applied and Pure Mathematics.
The researchers connected to the master's programme work in the area of Scientific Computing, more specific: large scale computational problems related to the numerical solution of partial differential equations. In the past five years this has led to special attention for the efficient and accurate solution of (very) large sparse linear systems, various types of eigenproblems, adaptive grid techniques, wavelet approximations in more dimensions, and parallel computing aspects. The work is in part fundamental (e.g., the wavelet approximations and the convergence analysis for other iteratively constructed approximations), but the main stream of the research is application oriented. However, also the application oriented research leads often to new insights and new theorems as well. A paper from our group received a SIAG/LA award as one of the two most outstanding papers in applicable linear algebra published during 1993-96. The same paper was reprinted in SIAM Review because of its exceptional quality and potential significance to the entire SIAM community. Other publications led to exceptional high citation scores. Recently, two research books have been published one by Oxford University press and one by Cambridge University press. The wavelet research activity was honored by NWO through the so-called "Vernieuwingsimpuls".
In the list below, short descriptions are given of the research interests of the staff members. For more information, follow the links to their homepages. Dr. Rob Bisseling is the leader of the Master Scientific Computer programme.
started his research with the construction of preconditioners for large systems of linear equations. These so-called incomplete LU (ILU) preconditioners are, in combination with iterative methods, are widely used. He continued his research in iterative techniques for improving approximate solutions. This led to a number of popular methods that are used all over the world in large scale computational models for simulating electronic circuits, oil reservoir modelling, diffusion and advection problems, the study of the spread of pollution in the groundwater, magnetic fields in video, etc. is interested in parallel computing, sparse matrix computations, combinatorial scientific computing, and bioinformatics. He has recently written a book Parallel Scientific Computation: A Structured Approach using BSP and MPI, published by Oxford University Press, 2004. is interested in numerical methods for solving linear systems of equations and eigenvalue problems for high dimensional matrices. These type problems arise in sciences whenever (in)stabilities are subject of research: in Quantum Chemistry, Plasma Physics, Mechanics, long term climate research, Oceanography, etc.. is doing research in the field of multiscale methods for solving partial differential equations. In particular, he works on adaptive finite element and wavelet discretizations of such equations, on the construction of wavelet bases on general domains or manifolds, and on multigrid methods for solving the arising linear systems. works on adaptive moving mesh methods for time-dependent partial differential equations. These methods are especially useful for models with steep moving transitions in the solutions (high temperature gradients, rotating or oscillating pulses, shocks, etc), wave-type equations (travelling waves, solitons, etc) and models with internal and boundary layer solutions. Applications stem from meteorology, astrophysics, chemistry, hydrology, plasmaphysics, amd many other areas.