Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities
Calo, Victor M.
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Physical Sciences and Engineering (PSE) Division
Numerical Porous Media SRI Center (NumPor)
Applied Mathematics and Computational Science Program
Earth Science and Engineering Program
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AbstractThis 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.
CitationTelescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities 2015, 51:2744 Procedia Computer Science
JournalProcedia Computer Science
Conference/Event nameInternational Conference on Computational Science, ICCS 2002