A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities

Handle URI:
http://hdl.handle.net/10754/562704
Title:
A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities
Authors:
Paszyński, Maciej R.; Calo, Victor M. ( 0000-0002-1805-4045 ) ; Pardo, David
Abstract:
This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.
KAUST Department:
Applied Mathematics and Computational Science Program; Earth Science and Engineering Program; Numerical Porous Media SRI Center (NumPor); Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program
Publisher:
Elsevier
Journal:
Computers and Mathematics with Applications
Issue Date:
Apr-2013
DOI:
10.1016/j.camwa.2013.02.006
ARXIV:
arXiv:1212.1992
Type:
Article
ISSN:
08981221
Sponsors:
MP was supported by Polish National Science Center grants no NN 519 447739 and NN 519 405737. DP was partially funded by the Project of the Spanish Ministry of Sciences and Innovation MTM2010-16511, the Laboratory of Mathematics (UFI 11/52), and the Ibero-American Project CYTED 2011 (P711RT0278). MP and DP were partially supported by the Center for Numerical Porous Media at KAUST.
Additional Links:
http://arxiv.org/abs/arXiv:1212.1992v1
Appears in Collections:
Articles; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorPaszyński, Maciej R.en
dc.contributor.authorCalo, Victor M.en
dc.contributor.authorPardo, Daviden
dc.date.accessioned2015-08-03T11:02:15Zen
dc.date.available2015-08-03T11:02:15Zen
dc.date.issued2013-04en
dc.identifier.issn08981221en
dc.identifier.doi10.1016/j.camwa.2013.02.006en
dc.identifier.urihttp://hdl.handle.net/10754/562704en
dc.description.abstractThis paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.en
dc.description.sponsorshipMP was supported by Polish National Science Center grants no NN 519 447739 and NN 519 405737. DP was partially funded by the Project of the Spanish Ministry of Sciences and Innovation MTM2010-16511, the Laboratory of Mathematics (UFI 11/52), and the Ibero-American Project CYTED 2011 (P711RT0278). MP and DP were partially supported by the Center for Numerical Porous Media at KAUST.en
dc.publisherElsevieren
dc.relation.urlhttp://arxiv.org/abs/arXiv:1212.1992v1en
dc.subjectDirect solveren
dc.subjectFinite element methoden
dc.subjecth adaptationen
dc.subjectLinear computational costen
dc.subjectReutilizationen
dc.titleA direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularitiesen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentEarth Science and Engineering Programen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.identifier.journalComputers and Mathematics with Applicationsen
dc.contributor.institutionAGH University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunication, Department of Computer Science, al. A. Mickiewicza 30, 30-059 Krakow, Polanden
dc.contributor.institutionDepartment of Applied Mathematics, Statistics and Operational Research, University of the Basque Country UPV/EHU, Leioa, Spainen
dc.contributor.institutionIKERBASQUE (Basque Foundation for Science), Bilbao, Spainen
dc.identifier.arxividarXiv:1212.1992en
kaust.authorCalo, Victor M.en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.