A Parallel Multistage ILU Factorization Based on a Hierarchical Graph Decomposition | Zendy

Pascal Hé | Zendy; Yousef Saad | Zendy

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A Parallel Multistage ILU Factorization Based on a Hierarchical Graph Decomposition

Author(s) -

Pascal Hé,

Yousef Saad

Publication year - 2006

Publication title -

siam journal on scientific computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.674

H-Index - 147

eISSN - 1095-7197

pISSN - 1064-8275

DOI - 10.1137/040608258

Subject(s) - computer science , matrix decomposition , factorization , solver , adjacency matrix , scalability , incomplete lu factorization , decomposition , graph , lu decomposition , domain decomposition methods , parallel computing , theoretical computer science , algorithm , finite element method , ecology , eigenvalues and eigenvectors , physics , quantum mechanics , database , biology , thermodynamics , programming language

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.

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