On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers

Handle URI:
http://hdl.handle.net/10754/563761
Title:
On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers
Authors:
Collier, Nathaniel Oren; Dalcin, Lisandro ( 0000-0001-8086-0155 ) ; Calo, Victor M. ( 0000-0002-1805-4045 )
Abstract:
SUMMARY: We compare the computational efficiency of isogeometric Galerkin and collocation methods for partial differential equations in the asymptotic regime. We define a metric to identify when numerical experiments have reached this regime. We then apply these ideas to analyze the performance of different isogeometric discretizations, which encompass C0 finite element spaces and higher-continuous spaces. We derive convergence and cost estimates in terms of the total number of degrees of freedom and then perform an asymptotic numerical comparison of the efficiency of these methods applied to an elliptic problem. These estimates are derived assuming that the underlying solution is smooth, the full Gauss quadrature is used in each non-zero knot span and the numerical solution of the discrete system is found using a direct multi-frontal solver. We conclude that under the assumptions detailed in this paper, higher-continuous basis functions provide marginal benefits.
KAUST Department:
Numerical Porous Media SRI Center (NumPor); Applied Mathematics and Computational Science Program; Earth Science and Engineering Program; Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program
Publisher:
Wiley-Blackwell
Journal:
International Journal for Numerical Methods in Engineering
Issue Date:
17-Sep-2014
DOI:
10.1002/nme.4769
Type:
Article
ISSN:
00295981
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.authorCollier, Nathaniel Orenen
dc.contributor.authorDalcin, Lisandroen
dc.contributor.authorCalo, Victor M.en
dc.date.accessioned2015-08-03T12:09:14Zen
dc.date.available2015-08-03T12:09:14Zen
dc.date.issued2014-09-17en
dc.identifier.issn00295981en
dc.identifier.doi10.1002/nme.4769en
dc.identifier.urihttp://hdl.handle.net/10754/563761en
dc.description.abstractSUMMARY: We compare the computational efficiency of isogeometric Galerkin and collocation methods for partial differential equations in the asymptotic regime. We define a metric to identify when numerical experiments have reached this regime. We then apply these ideas to analyze the performance of different isogeometric discretizations, which encompass C0 finite element spaces and higher-continuous spaces. We derive convergence and cost estimates in terms of the total number of degrees of freedom and then perform an asymptotic numerical comparison of the efficiency of these methods applied to an elliptic problem. These estimates are derived assuming that the underlying solution is smooth, the full Gauss quadrature is used in each non-zero knot span and the numerical solution of the discrete system is found using a direct multi-frontal solver. We conclude that under the assumptions detailed in this paper, higher-continuous basis functions provide marginal benefits.en
dc.publisherWiley-Blackwellen
dc.subjectAsymptotic analysisen
dc.subjectCollocationen
dc.subjectComputational efficiencyen
dc.subjectFinite elementsen
dc.subjectIsogeometricen
dc.titleOn the computational efficiency of isogeometric methods for smooth elliptic problems using direct solversen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentEarth Science and Engineering Programen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.identifier.journalInternational Journal for Numerical Methods in Engineeringen
dc.contributor.institutionConsejo Nacional de Investigaciones Científicas y TécnicasSanta Fe, Argentinaen
dc.contributor.institutionUniversidad Nacional del LitoralSanta Fe, Argentinaen
dc.contributor.institutionOak Ridge National LaboratoryOak Ridge, TN, United Statesen
kaust.authorCollier, Nathaniel Orenen
kaust.authorDalcin, Lisandroen
kaust.authorCalo, Victor M.en
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