Show simple item record

dc.contributor.authorGarcia, D.
dc.contributor.authorPardo, D.
dc.contributor.authorDalcin, L.
dc.contributor.authorPaszynski, M.
dc.contributor.authorCollier, N.
dc.contributor.authorCalo, V.M.
dc.date.accessioned2016-12-07T11:04:09Z
dc.date.available2016-12-07T11:04:09Z
dc.date.issued2016-09-23
dc.identifier.issn0045-7825
dc.identifier.urihttp://hdl.handle.net/20.500.11824/331
dc.description.abstractWe 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.sponsorshipThe Project of the Spanish Ministry of Economy and Competitiveness MTM2016-76329-R. The Consolidated Research Group Grant IT649-13 on "Mathematical Modeling, Simulation, and Industrial Applications (M2SI)", The ICERMAR Project KK-2015/0000097.en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectIsogeometric Analysis (IGA)en_US
dc.subjectFinite Element Analysis (FEA)en_US
dc.subjectrefined Isogeometric Analysis (rIGA)en_US
dc.subjectDirect solversen_US
dc.subjectMulti-frontal solversen_US
dc.subjectk-refinementen_US
dc.titleThe value of continuity: Refined isogeometric analysis and fast direct solversen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1016/j.cma.2016.08.017
dc.relation.publisherversionhttp://dx.doi.org/10.1016/j.cma.2016.08.017en_US
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/H2020/644202en_US
dc.relation.projectIDES/1PE/SEV-2013-0323en_US
dc.relation.projectIDES/1PE/MTM2016-76329-Ren_US
dc.relation.projectIDES/1PE/MTM2013-40824-Pen_US
dc.relation.projectIDEUS/BERC/BERC.2014-2017en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleComputer Methods in Applied Mechanics and Engineeringen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

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