Direct solvers performance on hadapted grids
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2015Collection
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We analyse the performance of direct solvers when applied to a system of linear equations arising from an hadapted, <sup>C0</sup> finite element space. Theoretical estimates are derived for typical hrefinement patterns arising as a result of a point, edge, or face singularity as well as boundary layers. They are based on the elimination trees constructed specifically for the considered grids. Theoretical estimates are compared with experiments performed with MUMPS using the nesteddissection algorithm for construction of the elimination tree from METIS library. The numerical experiments provide the same performance for the cases where our trees are identical with those constructed by the nesteddissection algorithm, and worse performance for some cases where our trees are different. We also present numerical experiments for the cases with mixed singularities, where how to construct optimal elimination trees is unknown. In all analysed cases, the use of hadaptive grids significantly reduces the cost of the direct solver algorithm per unknown as compared to uniform grids. The theoretical estimates predict and the experimental data confirm that the computational complexity is linear for various refinement patterns. In most cases, the cost of the direct solver per unknown is lower when employing anisotropic refinements as opposed to isotropic ones.
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