Clustered Edge-By-Edge Preconditioners For Non-Symmetric Finite Element Equations

Abstract

. In this paper we present new preconditioners for implicit edge-based computations inspired on the concept of clustered element-by-element preconditioners. These new globally defined preconditioners employ product decompositions of clusters of edges matrices obtained from the grouping of edges into superedges. A performance study of these new preconditioners is performed on the CRAY J90 parallel computer. We analyse several flow problems discretized by the SUPG formulation using GMRES as iterative driver. Catabriga, Martins, Coutinho and Alves 1 INTRODUCTION Parallel supercomputers are nowadays widely used in large-scale finite element flow simulations. Several examples may be found, for instance, in Tezduyar. 1 In such large-scale problems, the solution of nonlinear systems of equations involving millions of unknowns may be required. In these cases, Krylov space based iterative update techniques 2 are used for the solution of the equation systems arising from finite element di..