Direct solvers performance on h-adapted grids
MetadataShow full item record
We analyse the performance of direct solvers when applied to a system of linear equations arising from an h-adapted, <sup>C0</sup> finite element space. Theoretical estimates are derived for typical h-refinement 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 nested-dissection 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 nested-dissection 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 h-adaptive 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.
Showing items related by title, author, creator and subject.
Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive GridsAbouEisha, H.; Calo, Victor; Jopek, K.; Moshkov, M.; Paszynska, A.; Paszynski, M. (2018)The hp-adaptive Finite Element Method (hp-FEM) generates a sequence of adaptive grids with different polynomial orders of approximation and element sizes. The hp-FEM delivers exponential convergence of the numerical error ...
Element Partition Trees for H-Refined Meshes to Optimize Direct Solver Performance. Part I: Dynamic ProgrammingAboueisha, H.; Calo, Victor; Jopek, K.; Moshkov, M.; Paszynka, A.; Paszynski, M.; Skotniczny, M. (2017)We consider a class of two- and three-dimensional h-refined meshes generated by an adaptive finite element method. We introduce an element partition tree, which controls the execution of the multi-frontal solver algorithm ...
Dynamic programming algorithm for generation of optimal elimination trees for multi-frontal direct solver over h-refined gridsAbouEisha, H.; Moshkov, M.; Calo, Victor; Paszynski, M.; Goik, D.; Jopek, K. (2014)In this paper we present a dynamic programming algorithm for finding optimal elimination trees for computational grids refined towards point or edge singularities. The elimination tree is utilized to guide the multi-frontal ...