ABSTRACT
GUNDOLF HAASE and ULRICH LANGER Department of Mathematics , Technical University of Chemnitz, D-09009 Chemnitz , Germany
Abstract . Domain Decomposition (DD) techniques are not only the basic tools for data partitioning but also methods for constructing new parallel PDE solvers . Do main Decomposition, mesh adapt ion and load balance seem to be in contradiction to the efficient use of massively parallel computers with serveral hundred, or even sever al thousand powerful, distributed memory processors . In the case of plane boundary value problems producing solutions with fixed singularities caused by corner points at the boundary, by changing boundary conditions , or nonsmooth interfaces , it is possible to construct highly efficient , load balanced solvers based on non-overlapping DD tech niques . The finite element discretization uses Courant 's element on graded triangular meshes adapted to the singularities arising. The finite element equations are solved by the conjugate gradient method parallelized and preconditioned by DD techniques. The use of modified BPS preconditioners on the coupling boundaries and local multigrid methods with zero and specially chosen non-zero initial guesses in various Dirichlet DD preconditioners is studied. The numerical experiments carried out on transputer systems confirm the high efficiency of the parallel DD solvers proposed.
