Renumbering strategies based on multilevel techniques combined with ILU decompositions
The authors present an incomplete factorization technique that uses a renumbering of the unknowns, based on a sequence of grids as in a multigrid method. Also, a similar preconditioning technique is described, which can be used for matrices with arbitrary sparsity patterns as those arising from finite element methods on unstructured grides. During the factorization, the authors use a reordering to guarantee that the diagonal blocks to be inverted remain strongly diagonally dominant. This makes it possible to approximate the needed inverses by only one diagonal matrix, leading to more potential parallelism. The method is demonstrated for a number of test problems.
scientific article; zbMATH DE number 1467915