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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

Citations:

Zbl 0654.00011