Multi-threaded Nested Filtering Factorization Preconditioner

Abstract

The scalability and robustness of a class of non-overlapping domain decomposition preconditioners using 2-way nested dissection reordering is studied. In particular, three methods are considered: a nested symmetric successive over-relaxation (NSSOR), a nested version of modified ILU with rowsum constraint (NMILUR), and nested filtering factorization (NFF). The NMILUR preconditioner satisfies the rowsum property i.e., a right filtering condition on the vector (1, …, 1)^T. The NFF method is more general in the sense that it satisfies right filtering condition on any given vector. There is a subtle difference between NMILUR and NFF, but NFF is much more robust and converges faster than NSSOR and NMILUR. The test cases consist of a Poisson problem and convection-diffusion problems with jumping coefficients.