Multiprocessor sparse LU decomposition with controlled fill-in
During L/U decompositions of a sparse matrix, it is possible to perform computation on many diagonal elements simultaneously. Pivots that can be processed in parallel are related by a compatibility relation and are grouped in a compatible set. The collection of all maximal compatibles yields different maximum sized sets of pivots that can be processed in parallel. Generation of the maximal compatibles is based on the construction of an incompatible table, which gives information about pairs of incompatible table, algorithm to generate all maximal compatibles involves a binary tree search and is exponential in the order of the matrix. A technique for obtaining an ordered compatible set directly from the ordered incompatible table is given. This technique generates a set of compatible pivots with the property of generating few fills. A new heuristic algorithm is presented that combines the idea of an ordered compatible set with a limit binary tree search to generate several sets of compatible pivots in linear time. The parallel pivoting technique presented is a stepwise algorithm and can be applied to any submatrix of the original matrix. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices and on the HEP multiprocessor are presented and analyzed.
- Research Organization:
- Colorado Univ., Boulder (USA)
- OSTI ID:
- 6891551
- Country of Publication:
- United States
- Language:
- English
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