A Multi-Level Method for Solving General Sparse Matrices

Jun Zhang
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506--0046, USA


The innermost computational kernel of many large scale scientific and industrial numerical simulations is often to solve a large sparse linear system, which typically consumes more than 80% of the overall computational time. It is estimated that more than 70% of the supercomputer time is currently used for solving very large linear systems. We introduce a parallelizable multi-level block incomplete LU factorization technique for solving general sparse linear systems. The preconditioner was constructed by using recursive block incomplete factorization from the original matrix, It has a multi-level structure, possesses inherent parallelism, and exhibits certain properties that are typically enjoyed by multigrid methods. In this talk, we will focus on the use of large blocks as pivoting entries in constructing such preconditioner and discuss strategies to insure sparsity of the resulting preconditioner. Numerical results, including some very hard test problems from CFD applications, are presented to show that the new preconditioner is more robust and converges faster than some more traditional ILU-type preconditioners.

Return to Numerical Analysis and Scientific Computing Seminar.