The effect of a threshold variant TPABLO of the permutation (and partitioning) algorithm PABLO on the performance of certain preconditionings is explored. The goal of these permutations is to produce matrices with dense diagonal blocks, and in the threshold variant, with large entries in the diagonal blocks. Experiments are reported using matrices arising from the discretization of elliptic partial differential equations. The iterative solvers used are GMRES, QMR, BiCGStab and CGNR. The preconditioners are different incomplete factorizations. it is shown that preprocessing the matrices with TPABLO has a positive effect on the overall performance, resulting in better convergence rates for highly nonsymmetric problems.
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