dc.contributor.author Garcia, D. dc.contributor.author Pardo, D. dc.contributor.author Dalcin, L. dc.contributor.author Paszynski, M. dc.contributor.author Collier, N. dc.contributor.author Calo, V.M. dc.date.accessioned 2016-12-07T11:04:09Z dc.date.available 2016-12-07T11:04:09Z dc.date.issued 2016-09-23 dc.identifier.issn 0045-7825 dc.identifier.uri http://hdl.handle.net/20.500.11824/331 dc.description.abstract We propose the use of highly continuous finite element spaces interconnected with low continuity hyperplanes to maximize the performance of direct solvers. Starting from a highly continuous Isogeometric Analysis (IGA) discretization, we introduce $C^0$-separators to reduce the interconnection between degrees of freedom in the mesh. By doing so, both the solution time and best approximation errors are simultaneously improved. We call the resulting method refined Isogeometric Analysis (rIGA)". To illustrate the impact of the continuity reduction, we analyze the number of Floating Point Operations (FLOPs), computational times, and memory required to solve the linear system obtained by discretizing the Laplace problem with structured meshes and uniform polynomial orders. Theoretical estimates demonstrate that an optimal continuity reduction may decrease the total computational time by a factor between $p^2$ and $p^3$, with $p$ being the polynomial order of the discretization. Numerical results indicate that our proposed rIGA method delivers a speed-up factor proportional to $p^2$. In a $2D$ mesh with four million elements and $p = 5$, the linear system resulting from rIGA is solved $22$ times faster than the one from highly continuous IGA. In a $3D$ mesh with one million elements and $p = 3$, the linear rIGA system is solved $15$ times faster than the IGA one. en_US dc.description.sponsorship The Project of the Spanish Ministry of Economy and Competitiveness MTM2016-76329-R. en_US The Consolidated Research Group Grant IT649-13 on "Mathematical Modeling, Simulation, and Industrial Applications (M2SI)", The ICERMAR Project KK-2015/0000097. dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Isogeometric Analysis (IGA) en_US dc.subject Finite Element Analysis (FEA) en_US dc.subject refined Isogeometric Analysis (rIGA) en_US dc.subject Direct solvers en_US dc.subject Multi-frontal solvers en_US dc.subject k-refinement en_US dc.title The value of continuity: Refined isogeometric analysis and fast direct solvers en_US dc.type info:eu-repo/semantics/article en_US dc.identifier.doi 10.1016/j.cma.2016.08.017 dc.relation.publisherversion http://dx.doi.org/10.1016/j.cma.2016.08.017 en_US dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/644202 en_US dc.relation.projectID ES/1PE/SEV-2013-0323 en_US dc.relation.projectID ES/1PE/MTM2016-76329-R en_US dc.relation.projectID ES/1PE/MTM2013-40824-P en_US dc.relation.projectID EUS/BERC/BERC.2014-2017 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US dc.journal.title Computer Methods in Applied Mechanics and Engineering en_US
﻿

### This item appears in the following Collection(s)

Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España