Multi-threaded Nested Filtering Factorization Preconditioner

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.