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 is exact with the coefficient matrix on the vector of all ones. The NFF method is more general and it is exact on the coefficient matrix 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 equation and convection-diffusion problems with jumping coefficients.