The application of the non-overlapping domain decomposition to large scale finite element problems is a succesfull approach to parallelize the solution method for MIMD parallel computers. The method involves two technical steps. The first one is the partitioning of the complex geometry into an appropriate number of disjoint subdomains. The second is the solution of the local and the global problem.

Primal and dual substructuring methods are developed for efficient and scalable iterative solution of linear systems arising from the discretization of plate bending problems. The primal substructuring method is based on the Schur-Complement decomposition. The local problem can be solved directly or iteratively and completely in parallel. The global problem (in the displacements of the coupling nodes) has to be solved efficiently iteratively only. The dual method introduces Lagrange multipliers (forces) to ensure the compatibility between displacements in completely decoupled substructures. The additional, dual global problem is solved iteratively, too.

Computational kernels and the resulting solution properties are shown for the application of this family of solvers. The efficiency of the dual substructuring method for plate bending problems is demonstrated. Details of a portable implementation with MPI will be shown and results for Cray T3D and PowerPC will be compared.

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