A PARALLEL SOLVER BASED ON THE DUAL SCHUR DECOMPOSITION OF GENERAL FINITE-ELEMENT MATRICES

A parallel solver based on domain decomposition is presented for the s olution of large algebraic systems arising in the finite element discr etization of mechanical problems. It is hybrid in the sense that it co mbines a direct factorization of the local subdomain problems with an iterative treatment of the interface system by a parallel GMRES algori thm. An important feature of the proposed solver is the use of a set o f Lagrange multipliers to enforce continuity of the finite element unk nowns at the interface. A projection step and a preconditioner are pro posed to control the conditioning of the interface matrix. sThe decomp osition of the finite element mesh is formulated as a graph partitioni ng problem. A two-step approach is used where an initial decomposition is optimized by non-deterministic heuristics to increase the quality of the decomposition. Parallel simulations of a Navier-Stokes flow pro blem carried out on a Convex Exemplar SPP system with 16 processors sh ow that the use of optimized decompositions and the preconditioning st ep are keys to obtaining high parallel efficiencies. Typical parallel efficiencies range above 80%. (C) 1998 John Wiley gr Sons, Ltd.