Parallel and vectorial solving of finite element problems on a shared-memory multiprocessor

Some alternatives for speeding up finite-element computations by use of a vector-parallel shared memory multiprocessor are presented. The whole solution process is dealt with, including the calculation of element contributions (integration), global matrix construction (assembly), and resolution of the large sparse linear systems thus arising. The vector-parallel algorithms are implemented and compared on an Alliant FX/80, providing an automatic compiler, thus making parallel programming easier. The best choice between the possible combinations of the algorithms presented is discussed, considering the global performances. The ICCG (incomplete Cholesky preconditioned conjugate gradient) method, associated with parallel assembly and vectorial integration on finite elements, is the best for smooth problems. With nearly singular matrices, or when a smaller residual on the solution is needed, the direct method gives less time-expensive solutions