Large scale finite element computations with GMRES-like methods on a CRAY Y-MP

Abstract

GMRES-like methods require the computation and storage of basis vectors of Krylov subspaces. The number of vectors that has to be computed and stored depends on the number of iterations that has to be performed, that is if no restart or truncation strategy is employed. The number of iterations can be reduced by performing more matrix-vector multiplications per iteration, for example by applying a polynomial preconditioner or by performing inner iterations. In this paper we discuss this approach and we compare some of the resulting GMRES methods. The experimental comparison has been made on a CRAY Y-MP, using the finite element code DIANA. The element-by-element matrix-vector multiplication is discussed in detail.