On Minimization of Nonlinear Energies Using FEM in MATLAB

0584116 - ÚTIA 2024 RIV CH eng C - Conference Paper (international conference)
Moskovka, A. - Valdman, Jan - Vohnoutová, M.
On Minimization of Nonlinear Energies Using FEM in MATLAB.
Parallel Processing and Applied Mathematics : 14th International Conference, PPAM 2022. Cham: Springer, 2023 - (Wyrzykowski, R.; Dongarra, J.; Deelman, E.; Karczewski, K.), s. 331-342. Lecture Notes in Computer Science, 13827. ISBN 978-3-031-30444-6. ISSN 0302-9743. E-ISSN 1611-3349.
[International Conference on Parallel Processing and Applied Mathematics (PPAM 2022) /14./. Gdansk (PL), 11.09.2022-14.09.2022]
R&D Projects: GA MŠMT 8J21AT001; GA ČR GF21-06569K
Institutional support: RVO:67985556
Keywords : minimization * nonlinear energy * finite elements * Ginzburg-Landau model * topology optimization
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
http://library.utia.cas.cz/separaty/2024/MTR/moskovka-0584116.pdf

Two minimization problems are added to the Moskovka and Valdman MATLAB package (2022): a Ginzburg-Landau (scalar) problem and a topology optimization (both scalar and vector) problem in linear elasticity. Both problems are described as nonlinear energy minimizations that contain the first gradient of the unknown field. Their energy functionals are discretized by finite elements, and the corresponding minima are searched using the trust-region method with a known Hessian sparsity or the Quasi-Newton method.
Permanent Link: https://hdl.handle.net/11104/0352092