Domain Decomposition vs

Domain Decomposition (DD) techniques are not only the basic tools for data partitioning but also methods for constructing new parallel pde solvers. Domain Decomposition, mesh adaption and load balance seem to be in contradiction to the eecient use of massively parallel computers with serveral hundered, or even several thousand powerful, distributed memory processors. In the case of plane boundary value problems producing solutions with xed singularities caused by corner points at the boundary, by changing boundary conditions, or nonsmooth interfaces, it is possible to construct highly eecient, load balanced solvers based on non-overlapping DD techniques. The nite element discretization uses Courant's element on graded triangular meshes adapted to the singularities arizing. The nite element equations are solved by the conjugate gradient method parallelized and preconditioned by DD techniques. The use of modiied BPS precondi-tioners on the coupling boundaries and local multigrid methods with zero and specially chosen non-zero initial guesses in various Dirichlet DD precon-ditioners is studied. The numerical experiments carried out on transputer systems connrm the high eeciency of the parallel DD solvers proposed.