Parallel preconditioners based on partitioning sparse matrices 1
Iain Duff, S Riyavong, Martin B. van Gijzen · Technical report. RAL - Council for the Central Laboratory of the Research Councils · 2004
We describe a method for constructing an ecien t block diagonal preconditioner for accelerating the iterative solution of general sets of sparse linear equations. Our method uses a hypergraph partitioner on a scaled and sparsied matrix and attempts to ensure that the diagonal blocks are nonsingular and dominant. We illustrate our approach using the partitioner PaToH and the Krylov-based GMRES algorithm. We verify our approach with runs on problems from economic modelling and chemical engineering, traditionally dicult applications for iterative methods. Our approach and the block diagonal preconditioning lends itself to good exploitation of parallelism. This we also demonstrate.