Parallel preconditioned conjugate-gradient type algorithms for general sparsity structures

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.

Keywords:

• Nonsymmetric systems
• iterative methods
• conjugate gradient
• preconditioning
• vector processor
• parallel processor
• shared memory

C.R. CATEGORIES::

• G.1.8
• G.1.3.