PT-Scotch: A tool for efficient parallel graph ordering
Parallel Computing
Journal of Computational Physics
Modification and Compensation Strategies for Threshold-based Incomplete Factorizations
SIAM Journal on Scientific Computing
A Robust Two-Level Incomplete Factorization for (Navier-)Stokes Saddle Point Matrices
SIAM Journal on Matrix Analysis and Applications
HPCC'07 Proceedings of the Third international conference on High Performance Computing and Communications
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PHIDAL (parallel hierarchical interface decomposition algorithm) is a parallel incomplete factorization method which exploits a hierarchical interface decomposition of the adjacency graph of the coefficient matrix. The idea of the decomposition is similar to that of the well-known wirebasket techniques used in domain decomposition. However, the method is devised for general, irregularly structured, sparse linear systems. This paper describes a few algorithms for obtaining good quality hierarchical graph decompositions and discusses the parallel implementation of the factorization procedure. Numerical experiments are reported to illustrate the scalability of the algorithm and its effectiveness as a general purpose parallel linear system solver.