Direct Methods for Unsymmetric Blockwise Sparse Matrices: Application to Domain Decomposition Global Preconditioning

摘要

A memory and time efficient block-wise sparse LU factorization and forward/backward(F/B) substitution for the application of the W-FETI (Woodbury-FETI) global algebraic Domain Decomposition preconditioner is presented. The proposed direct solver exploits inherited block-wise sparsity (sparse collection of dense block submatrices) of the unsymmetric W-FETI matrix, reducing memory and attaining high degree of cache coherency and maximal BLAS Level 3 performance. Comparisons with state-of-the-art sparse direct solvers on various electrically large problems suggest up to 3 times less memory and run-time complexity for the factorization and for the multiple rhs F/B substitution part, while maintaining the same accuracy.