Preconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficients

Handle URI:
http://hdl.handle.net/10754/563970
Title:
Preconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficients
Authors:
Gao, Longfei; Calo, Victor M. ( 0000-0002-1805-4045 )
Abstract:
In this paper, we combine the Alternating Direction Implicit (ADI) algorithm with the concept of preconditioning and apply it to linear systems discretized from the 2D steady-state diffusion equations with orthotropic heterogeneous coefficients by the finite element method assuming tensor product basis functions. Specifically, we adopt the compound iteration idea and use ADI iterations as the preconditioner for the outside Krylov subspace method that is used to solve the preconditioned linear system. An efficient algorithm to perform each ADI iteration is crucial to the efficiency of the overall iterative scheme. We exploit the Kronecker product structure in the matrices, inherited from the tensor product basis functions, to achieve high efficiency in each ADI iteration. Meanwhile, in order to reduce the number of Krylov subspace iterations, we incorporate partially the coefficient information into the preconditioner by exploiting the local support property of the finite element basis functions. Numerical results demonstrated the efficiency and quality of the proposed preconditioner. © 2014 Elsevier B.V. All rights reserved.
KAUST Department:
Applied Mathematics and Computational Science Program; Numerical Porous Media SRI Center (NumPor); Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program
Publisher:
Elsevier BV
Journal:
Journal of Computational and Applied Mathematics
Issue Date:
Jan-2015
DOI:
10.1016/j.cam.2014.06.021
Type:
Article
ISSN:
03770427
Sponsors:
This work was supported in part by the King Abdullah University of Science and Technology (KAUST) Center for Numerical Porous Media and by an Academic Excellence Alliance program award from KAUST's Global Collaborative Research under the title "Seismic wave focusing for subsurface imaging and enhanced oil recovery".
Appears in Collections:
Articles; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorGao, Longfeien
dc.contributor.authorCalo, Victor M.en
dc.date.accessioned2015-08-03T12:21:21Zen
dc.date.available2015-08-03T12:21:21Zen
dc.date.issued2015-01en
dc.identifier.issn03770427en
dc.identifier.doi10.1016/j.cam.2014.06.021en
dc.identifier.urihttp://hdl.handle.net/10754/563970en
dc.description.abstractIn this paper, we combine the Alternating Direction Implicit (ADI) algorithm with the concept of preconditioning and apply it to linear systems discretized from the 2D steady-state diffusion equations with orthotropic heterogeneous coefficients by the finite element method assuming tensor product basis functions. Specifically, we adopt the compound iteration idea and use ADI iterations as the preconditioner for the outside Krylov subspace method that is used to solve the preconditioned linear system. An efficient algorithm to perform each ADI iteration is crucial to the efficiency of the overall iterative scheme. We exploit the Kronecker product structure in the matrices, inherited from the tensor product basis functions, to achieve high efficiency in each ADI iteration. Meanwhile, in order to reduce the number of Krylov subspace iterations, we incorporate partially the coefficient information into the preconditioner by exploiting the local support property of the finite element basis functions. Numerical results demonstrated the efficiency and quality of the proposed preconditioner. © 2014 Elsevier B.V. All rights reserved.en
dc.description.sponsorshipThis work was supported in part by the King Abdullah University of Science and Technology (KAUST) Center for Numerical Porous Media and by an Academic Excellence Alliance program award from KAUST's Global Collaborative Research under the title "Seismic wave focusing for subsurface imaging and enhanced oil recovery".en
dc.publisherElsevier BVen
dc.subjectAlternating Direction Impliciten
dc.subjectCompound iterationen
dc.subjectFinite element methoden
dc.subjectKronecker producten
dc.subjectPreconditioningen
dc.subjectTensor product basis functionsen
dc.titlePreconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficientsen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science 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.journalJournal of Computational and Applied Mathematicsen
kaust.authorCalo, Victor M.en
kaust.authorGao, Longfeien
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.