MODELING WITH COLLABORATING PDE SOLVERS - THEORY AND PRACTICE

We consider the problem of modeling very complex physical systems by a network of collaborating PDE solvers. Various aspects of this problem are examined from the points of view of real applications, modern computer science technology, and their impact on numerical methods. The related methodologies include network of collaborating software modules, object-oriented programming and domain decomposition. We present an approach which combines independent PDE solvers for simple domains which collaborate using interface relaxation to solve complex problems. The mathematical properties and application examples are discussed. A software system RELAX is described which is implemented as a platform to test various relaxers and to solve complex problems using this approach. Both theory and practice show that this is a promising approach for efficiently solving complicated problems on modern computer environments