Parallel Schur Complement Techniques Based on Multiprojection Methods

Abstract

The simulation of several physical phenomena, arising from a wide class of scientific fields, requires solving large sparse linear systems effectively. In order to exploit appropriately the available supercomputing infrastructures, designing efficient and scalable solvers for large sparse linear systems is necessary. A hybrid parallel algebraic iterative method based on the Schur complement method and multiprojection techniques that utilizes semiaggregated subdomains is proposed. The graph corresponding to the coefficient matrix of the sparse linear system is partitioned by a graph partitioning algorithm and the Schur complement problem is solved by a preconditioned Krylov subspace method. The preconditioning scheme is based on domain decomposition and the resulting subdomains consist of fine and aggregated components from the inner boundaries. Moreover, two variants for approximating the local Schur complements, derived from the semiaggregation procedure, are proposed in order to improve memory requirements and preprocessing time. The proposed method is suitable for distributed memory systems with multicore nodes and has improved convergence behavior for a large number of workstations. Numerical and comparative results concerning the applicability, the convergence behavior, and the parallel performance of the proposed scheme are given.