Fast FEM evaluation of nonlinear energies: nodal elements

Version 2.2.4 (114 KB) by Alexej Moskovka
Vectorized evaluation of nonlinear energies and their gradients using P1 finite elements and application to energy minimizations.
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Updated 14 Jul 2025

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This code provides computational benchmarks from the papers:
Alexej Moskovka and Jan Valdman: Fast MATLAB evaluation of nonlinear energies using FEM in 2D and 3D: nodal elements, Applied Mathematics and Computation, Vol. 424, 2022
https://doi.org/10.1016/j.amc.2022.127048
and
Alexej Moskovka, Jan Valdman, and Marta Vohnoutová: On minimization of nonlinear energies using FEM in MATLAB, PPAM 2022, Lecture Notes in Computer Science (LNCS) 13827, pp. 331–342, 2023
https://doi.org/10.1007/978-3-031-30445-3_28
Please cite the papers if you find the code useful.

Cite As

Alexej Moskovka and Jan Valdman (2022). Fast FEM evaluation of nonlinear energies: nodal elements (https://www.mathworks.com/matlabcentral/fileexchange/97889), MATLAB Central File Exchange. Retrieved May 10, 2022.

MATLAB Release Compatibility
Created with R2018a
Compatible with any release
Platform Compatibility
Windows macOS Linux
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benchmark1

benchmark2

benchmark3

benchmark4

benchmark5

benchmark6

benchmark7

benchmark8

benchmark8/models

library_assemblies_nodal

library_elasticity

library_evaluate

library_integration

library_meshing

library_meshing/algebra

library_meshing/domains/2D

library_meshing/domains/3D

library_mix

library_vectorization_faster

library_visualization

Version Published Release Notes
2.2.4

DOI link to the second paper has been added.
2.2.3

The comments inside some functions have been modified.
2.2.2

Formulas for p-Laplace energy and its explicit gradient have been corrected.

Performance of "preprocessingNodalPatches" functions (both 2D and 3D) has been improved.
2.2.1

Newly, the Topology Optimization solver allows to compute several mesh refinement levels and generates a table with energy values and evaluation times.
2.2.0

The contents of the original folders have been restructured. The total number of files has been significantly decreased
2.1.0

The Ginzburg-Landau problem and the Topology optimization problem have been added
1.1.1

DOI of the published paper has been added to the description.
The citation has been updated.
1.1.0

The performance of the codes has been improved. Additionally, the contents of individual folders have been slightly restructured for better clarity.
1.0.0