Application of sparse matrix solvers as effective preconditioners

Abstract

In this paper the use of a new out-of-core sparse matrix package for the numerical solution of partial differential equations involving complex geometries arising from aerospace applications is discussed. The sparse matrix solver accepts contributions to the matrix elements in random order and assembles the matrix using fast sort/merge routines. Fill-in is reduced through the use of a physically based nested dissection ordering. For very large problems a drop tolerance is used during the matrix decomposition phase. The resulting incomplete factorization is an effective preconditioner for Krylov subspace methods, such as GMRES. Problems involving 200,000 unknowns routinely are solved on the Cray X-MP using 64MW of solid-state storage device (SSD).