Some Aspects of Parallel Implementation of the Finite Element Method on Message Passing Architectures

Abstract
Discussed are some aspects of implementing the finite element method on parallel computers with local memory and message passing. In particular, the costs of using high order and low order elements, and of direct and iterative solvers are compared for solving the linear systems that occur. Our model of parallel computation is a two-dimensional grid of processors chosen to be similar in shape to the underlying grid. Our main conclusions are that sparse direct solvers generalize naturally to methods based on high order elements, and that direct solvers are adequate for two-dimensional problems, especially for multiple load vectors. High order methods are shown to achieve higher accuracy at less cost on some typical model problems.

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