MATLAB Implementation of Hp Finite Elements on Rectangles Using Hierarchical Basis Functions

0584111 - ÚTIA 2024 RIV CH eng C - Conference Paper (international conference)
Moskovka, A. - Valdman, Jan
MATLAB Implementation of Hp Finite Elements on Rectangles Using Hierarchical Basis Functions.
Parallel Processing and Applied Mathematics : 14th International Conference, PPAM 2022. Cham: Springer, 2023 - (Wyrzykowski, R.; Dongarra, J.; Deelman, E.; Karczewski, K.), s. 287-299. 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 : MATLAB vectorization * finite elements * mass and stiffness matrices * uniform hp-refinement * boundary value problem
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-0584111.pdf

A MATLAB implementation of hierarchical shape functions on 2D rectangles is explained and available for download. Global shape
functions are ordered for a given polynomial degree according to the indices of the nodes, edges, or elements to which they belong. For a uniform p-refinement, the hierarchical structure enables an effective assembly of mass and stiffness matrices. A solution to a boundary value problem is approximated for various levels of uniform h and p refinements.
Permanent Link: https://hdl.handle.net/11104/0352090