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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F22%3A00563205" target="_blank" >RIV/67985556:_____/22:00563205 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/49777513:23520/22:43965839 RIV/60076658:12310/22:43904868

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0096300322001345?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0096300322001345?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.amc.2022.127048" target="_blank" >10.1016/j.amc.2022.127048</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Applied Mathematics and Computation

ISSN

0096-3003

e-ISSN

1873-5649

Svazek periodika

424

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

18

Strana od-do

127048

Kód UT WoS článku

000794128400002

EID výsledku v databázi Scopus

2-s2.0-85126531727