Research description
Many scientific models for the simulation of continuous phenomena in Biology, Physics, and Technical applications, lead to the necessity to solve coupled systems of (partial) differential equations. This leads to a number of computational problems:

• After proper grids have been imposed, the model leads in most situations to a (non-)linear system that has to be solved. As the model becomes more realistic, these systems have typically a very large dimension, say in the order of a billion of unknowns. This requires iterative solvers. Many of the problems, for instance those involving constraints (biologic systems), or magnetic fields (Maxwell equations) lead to indefinite systems and such systems are extremely difficult to solve with iterative techniques. The aim is to solve these systems with preconditioning, for which we need to simplify the given model, guided by knowledge from the origin of the model.
• Many of the models depend critically on one or more parameters (local forces, temperature changes, changes in the electrical field) and in order to determine where exactly the sensitivity takes place, we need selective eigenvalue information of the system matrices. This can, in principle be done with tools developed in Utrecht (Jacobi-Davidson methods), but this requires also preconditioning, much in the same way, as in the previous item.
• Parallel Computing is absolutely necessary to compute the desired solutions of these models. This requires data-layouts that can be used, and adapted, for various parts of the model (the definition, the discretization, and the various numerical solvers).

Associate partners

• CWI
• Technische Universiteit Delft
• Universiteit Twente

MSV1.2 Researchers funded by BRICKS

• Prof.dr. H.A. van der Vorst (UU)
• Dr. G. Sleijpen (UU)
• Dr. R. Bisseling (UU)
• Dr. P. Zegeling (UU)

For more information, please refer to the publications and posters of this project.