Elsevier

Procedia Computer Science

Volume 51, 2015, Pages 2744-2748
Procedia Computer Science

Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities

https://doi.org/10.1016/j.procs.2015.05.415Get rights and content
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Abstract

This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver.

Keywords

hybrid solver
multi-frontal solver
h adaptive finite element method
ILUPCG
GALO

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Selection and peer-review under responsibility of the Scientific Programme Committee of ICCS 2015.