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

Handle URI:
http://hdl.handle.net/10754/556723
Title:
Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities
Authors:
Paszyńska, Anna; Jopek, Konrad; Banaś, Krzysztof; Paszyński, Maciej; Gurgul, Piotr; Lenerth, Andrew; Nguyen, Donald; Pingali, Keshav; Dalcind, Lisandro; Calo, Victor M. ( 0000-0002-1805-4045 )
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.
KAUST Department:
Center for Numerical Porous Media (NumPor); Applied Mathematics and Computational Science Program; Earth Science and Engineering Program
Citation:
Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities 2015, 51:2744 Procedia Computer Science
Journal:
Procedia Computer Science
Conference/Event name:
International Conference on Computational Science, ICCS 2002
Issue Date:
1-Jun-2015
DOI:
10.1016/j.procs.2015.05.415
Type:
Conference Paper
ISSN:
18770509
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S1877050915012235
Appears in Collections:
Conference Papers; Applied Mathematics and Computational Science Program; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorPaszyńska, Annaen
dc.contributor.authorJopek, Konraden
dc.contributor.authorBanaś, Krzysztofen
dc.contributor.authorPaszyński, Maciejen
dc.contributor.authorGurgul, Piotren
dc.contributor.authorLenerth, Andrewen
dc.contributor.authorNguyen, Donalden
dc.contributor.authorPingali, Keshaven
dc.contributor.authorDalcind, Lisandroen
dc.contributor.authorCalo, Victor M.en
dc.date.accessioned2015-06-10T18:40:46Zen
dc.date.available2015-06-10T18:40:46Zen
dc.date.issued2015-06-01en
dc.identifier.citationTelescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities 2015, 51:2744 Procedia Computer Scienceen
dc.identifier.issn18770509en
dc.identifier.doi10.1016/j.procs.2015.05.415en
dc.identifier.urihttp://hdl.handle.net/10754/556723en
dc.description.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.en
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S1877050915012235en
dc.rightsArchived with thanks to Procedia Computer Science, Under a Creative Commons license http://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjecthybrid solveren
dc.subjectmulti-frontal solveren
dc.subjecth adaptive finite element methoden
dc.subjectILUPCGen
dc.subjectGALOen
dc.titleTelescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularitiesen
dc.typeConference Paperen
dc.contributor.departmentCenter for Numerical Porous Media (NumPor)en
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentEarth Science and Engineering Programen
dc.identifier.journalProcedia Computer Scienceen
dc.conference.date2002-04-21 to 2002-04-24en
dc.conference.nameInternational Conference on Computational Science, ICCS 2002en
dc.conference.locationAmsterdam, NLDen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionJagiellonian University, Krakow, Polanden
dc.contributor.institutionAGH University of Science and Technology, Krakow, Polanden
dc.contributor.institutionInstitute for Computational and Engineering Sciences, (ICES), TX, USAen
kaust.authorDalcin, Lisandroen
kaust.authorCalo, Victor M.en
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