FACTORIZED SPARSE APPROXIMATE INVERSE PRECONDITIONING .2. SOLUTION OF3D FE SYSTEMS ON MASSIVELY-PARALLEL COMPUTERS

An iterative method for solving large linear systems with sparse symme tric positive definite matrices on massively parallel computers is sug gested. The method is based on the Factorized Sparse Approximate Inver se (FSAI) preconditioning of 'parallel' CG iterations. Efficiency of a concurrent implementation of the FSAI-CG iterations is analyzed for a model hypercube, and an estimate of the optimal hypercube dimension i s derived. For finite element applications, two strategies for selecti ng the preconditioner sparsity pattern are suggested. A high convergen ce rate of the resulting iterations is demonstrated numerically for th e 3D equilibrium equations for linear elastic orthotropic materials ap proximated using both h- and p-versions of the FEM.