Title:	Fast MATLAB evaluation of nonlinear energies using FEM in 2D and 3D: Nodal elements
Authors:	Moskovka, Alexej Valdman, Jan
Citation:	MOSKOVKA, 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: 0096-3003
Issue Date:	2022
Publisher:	Elsevier
Document type:	článek article
URI:	2-s2.0-85126531727 http://hdl.handle.net/11025/50628
ISSN:	0096-3003
Keywords in different language:	approximative gradient;finite element method;hyperelasticity;MATLAB;nonlinear energy minimization;vectorization
Abstract in different language:	Nonlinear 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.
Rights:	© Elsevier
Appears in Collections:	Články / Articles (KMA) OBD

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