An environment for the parallel solution of coupled problems on structured grids

Abstract

The solution of coupled problems is one of the grand challenges in scientific computing. Many problems can only be solved partially. Not all dependencies can be taken into account, e.g. only subproblems can be solved completely, even when optimal numerical methods (multigrid methods) are used. Therefore, parallel simulation is inevitable.

Coupled simulation of problems with different numerical complexities is possible now. An environment has been developed, which is an extension of L _i SS (environment for the parallel multigrid solution of partial differential equations on general 2D domains). Block-structured grids with overlap are the basis for parallelization. In order to achieve acceptable load-balance each subproblem is distributed to all processors. Components of the multigrid algorithm can be selected separately for each subproblem, thus allowing optimal methods for each problem. In addition, a large number of coupling strategies can be used, varying from coupling after each time step to coupling after each relaxation.

This strategy can be used in a real life example from VLSI wafer fabrication, where oxidation and diffusion are simulated coupled and in parallel.

This work was supported within the GRISSLi project by the German Federal Ministry for Research and Education under contract no. 01IS512C.