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

Result code in 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>
Alternative codes found
RIV/49777513:23520/22:43965839 RIV/60076658:12310/22:43904868
Result on the web
<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>

Result language
angličtina
Original language name
Fast MATLAB evaluation of nonlinear energies using FEM in 2D and 3D: Nodal elements
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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