Abstract
A parallel and vectorized multigrid algorithm is described and implemented on an Alliant FX/8 computer. The multigrid method, a fast iterative technique, is applied to the finite element solution of linear elastic solid mechanics problems. The necessary matrix-vector multiplications, which comprise a significant part of the solution time, are performed on the element level. This technique has two advantages: the storage requirements are low, since only the individual element are required (which can be computed when needed), and matrix-vector multiplications on the element level can easily be optimized on the Alliant FX/8. The greatest observed speed-up is 5.23 on 8 processors, which implies that at least 92% of the solution algorithm is parallelizable. The method can solve a problem with just over 2 000 000 degrees-of-freedom in about h with 200 Mbytes of storage on 8 processors.
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