Erhel, Jocelyne; Lichnewsky, Alain; Thomasset, François Vectorizing finite elements methods. (English) Zbl 0657.65047 Computers and computing, Proc. Int. Conf. dedic. N. Gastinel, Grenoble/France 1985, Étud. Rech. Inf., 255-269 (1986). [For the entire collection see Zbl 0654.00011.] This paper deals with some techniques we have developped to implement - on vector processors such as CRAY-IS, FUJITSU/VP200, HITACHI/S810,... - linear algebra algorithms for sparse matrices associated with finite element methods; the particular algorithm we consider here is preconditionned conjugate gradient. First of all we consider the case of “regular” matrix structures which we encounter in the context of finite difference methods, and we introduce a renumbering of unknowns in order to remove data dependencies. Then we extend this renumbering to the general case of finite element methods. Finally we present an optimization procedure based on Monte-Carlo techniques to improve the renumbering. MSC: 65F10 Iterative numerical methods for linear systems 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65Y05 Parallel numerical computation 65F50 Computational methods for sparse matrices 65C05 Monte Carlo methods Keywords:vector processors; sparse matrices; finite element methods; preconditionned conjugate gradient; finite difference methods; renumbering of unknowns; Monte-Carlo techniques Citations:Zbl 0654.00011 PDFBibTeX XML