Fast MATLAB evaluation of nonlinear energies using FEM in 2D and 3D: Nodal elements

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dc.contributor.authorMoskovka, Alexej
dc.contributor.authorValdman, Jan
dc.date.accessioned2022-12-12T11:00:33Z
dc.date.available2022-12-12T11:00:33Z
dc.date.issued2022
dc.description.abstract-translatedNonlinear energy functionals appearing in the calculus of variations can be discretized by the finite element (FE) method and formulated as a sum of energy contributions from local elements. A fast evaluation of energy functionals containing the first order gradient terms is a central part of this contribution. We describe a vectorized implementation using the simplest linear nodal (P1) elements in which all energy contributions are evaluated all at once without the loop over triangular or tetrahedral elements. Furthermore, in connection to the first-order optimization methods, the discrete gradient of energy functional is assembled in a way that the gradient components are evaluated over all degrees of freedom all at once. The key ingredient is the vectorization of exact or approximate energy gradients over nodal patches. It leads to a time-efficient implementation at higher memory-cost. Provided codes in MATLAB related to 2D/3D hyperelasticity and 2D p-Laplacian problem are available for download and structured in a way it can be easily extended to other types of vector or scalar forms of energies.en
dc.format18 s.cs
dc.format.mimetypeapplication/pdf
dc.identifier.citationMOSKOVKA, A. VALDMAN, J. Fast MATLAB evaluation of nonlinear energies using FEM in 2D and 3D: Nodal elements. APPLIED MATHEMATICS AND COMPUTATION, 2022, roč. 424, č. JUL 2022, s. nestránkováno. ISSN: 0096-3003cs
dc.identifier.document-number794128400002
dc.identifier.doi10.1016/j.amc.2022.127048
dc.identifier.issn0096-3003
dc.identifier.obd43936839
dc.identifier.uri2-s2.0-85126531727
dc.identifier.urihttp://hdl.handle.net/11025/50628
dc.language.isoenen
dc.project.IDSGS-2022-006/Kvalitativní a kvantitativní studium matematických modelů V.cs
dc.publisherElsevieren
dc.relation.ispartofseriesApplied Mathematics And Computationen
dc.rights© Elsevieren
dc.rights.accessopenAccessen
dc.subject.translatedapproximative gradienten
dc.subject.translatedfinite element methoden
dc.subject.translatedhyperelasticityen
dc.subject.translatedMATLABen
dc.subject.translatednonlinear energy minimizationen
dc.subject.translatedvectorizationen
dc.titleFast MATLAB evaluation of nonlinear energies using FEM in 2D and 3D: Nodal elementsen
dc.typečlánekcs
dc.typearticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen

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