Multithreaded Direction Preserving Preconditioners

The scalability and robustness of a class of nonoverlapping domain decomposition preconditioners using 2-way nested dissection reordering is studied. We consider two different factorizations: nested and block versions. Both these variants have advantages and disadvantages. The nested variants have less than half the memory requirements compared to block variants. On the other hand, the block variants have faster solve phase and converges within similar number of iterations. In particular, four methods are considered: a nested symmetric successive over relaxation (NSSOR), its block variant block SSOR (BSSOR), nested filtering factorization (NFF), and its block variant block filtering factorization (BFF). The recently introduced filtering preconditioners namely NFF and BFF are two filtering preconditioners that preserve direction on a given filter vector. The scalability and robustness of these methods are discussed on shared memory architecture. We outline the algorithmic differences between NFF and BFF. The implementation is recursive and cache oblivious. The test cases consist of a Poisson problem and convection-diffusion problems with jumping coefficients.