Parallel algorithms for the finite element method

Abstract

Existing finite element methods, algorithms and application programs have been developed in the milieu of the serial or single processor computer. Substantial efforts are currently being made to modify their computational aspects in order to take advantage of the power inherent in the newer generations of parallel multiprocessor computers. The parallelizing techniques being explored tend to be derived from or are closely related to serial concepts. Parallelism is difficult to achieve from this direction. The present work develops and implements a new class of parallel algorithms for the finite element method based upon the use of projections on finite-dimensional spaces. Projections provide a formal and general mechanism for decomposing or partitioning a problem into a col;ection of smaller related problems which can be treated in parallel. These algorithms can be programmed in a wholly asynchronous mode and have been implemented and studied on a shared memory multiprocessor computer with up to 24 processors. On large test problems they have been shown to produce almost perfect speedup and to be extremely efficient.