Direct construction of reciprocal mass matrix and higher order fininite element method

0568131 - ÚT 2024 CZ eng C - Konferenční příspěvek (zahraniční konf.)
Cimrman, Robert - Kolman, Radek - González, J. A. - Park, K. C.
Direct construction of reciprocal mass matrix and higher order fininite element method.
Seminar on Numerical Analysis & Winter School. Proceedings of the conference SNA'23. Ostrava: Institute of Geonics of the CAS, 2023 - (Starý, J.; Sysala, S.; Sysalová, D.), s. 8-11. ISBN 978-80-86407-85-2.
[SEMINAR ON NUMERICAL ANALYSIS - SNA /23./. Ostrava (CZ), 23.01.2023-27.01.2023]
Grant CEP: GA ČR GA23-06220S
Institucionální podpora: RVO:61388998
Klíčová slova: higher-order finite element method * reciprocal mass matrix * transient problems * explicit time integration * lumping process
Obor OECD: Applied mechanics
https://www.ugn.cas.cz/event/2023/sna/files/sna23-sbornik.pdf

When solving dynamical problems of computational mechanics, such as contact-impact problems or cases involving complex structures under fast loading conditions, explicit time-stepping algorithms are usually preferred over implicit ones. The explicit schemes are normally combined with the lumped (diagonal) mass matrix so that the calculations are efficient and moreover dispersion errors in wave propagation are partially eliminated. As an alternative to lumping with advantageous properties, the reciprocal mass matrix is an inverse mass matrix that has the same sparsity structure as the original consistent mass matrix, preserves the total mass, captures well the desired frequency spectrum and leads thus to efficient and accurate calculations. In the contribution we comment on the usability of the reciprocal mass matrix in connection with higher order FEM.
Trvalý link: https://hdl.handle.net/11104/0342432