Parallel preconditioned conjugate-gradient type algorithms for general sparsity structures

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Abstract
We discuss a parallel and vectorizable ILU type preconditioner for conjugate-gradient algorithms for problems with general sparsity patterns. The algorithm partitions the matrix in overlapping blocks, and performs local incomplete factorizations. The resulting algorithm typically requires a few iterations more to converge than its uniprocessor counterpart, but it has a very large granularity that makes it suitable for execution on coarse grain parallel systems with a high cost of synchronization. We obtain speed-ups of up to 3.3 on 4 processors compared to a good uniprocessor implementation on some problems from a finite element application.