Analysis of multilevel graph partitioning
Supercomputing '95 Proceedings of the 1995 ACM/IEEE conference on Supercomputing
Computing
Multilevel k-way partitioning scheme for irregular graphs
Journal of Parallel and Distributed Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Parallel design and performance of nested filtering factorization preconditioner
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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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.