Inverse mass matrix for higher-order finite element method via localized Lagrange multipliers

0518643 - ÚT 2020 RIV CZ eng A - Abstract
Kolman, Radek - González, J.A. - Kopačka, Ján - Cho, S.S. - Park, K.C.
Inverse mass matrix for higher-order finite element method via localized Lagrange multipliers.
Modelling 2019. Ostrava: Institute of Geonics of the Czech Academy of Sciences, 2019 - (Blaheta, R.; Starý, J.; Sysala, S.). s. 139-140. ISBN 978-80-86407-79-1.
[Modelling 2019: International conference on mathematical modelling and computational methods in applied sciences and engineering. 16.09.2019-20.09.2019, Olomouc]
R&D Projects: GA AV ČR(CZ) GA19-04956S; GA MŠMT(CZ) EF15_003/0000493
Institutional support: RVO:61388998
Keywords : direct inversion of mass matrix * finite element method * free-vibration problem
OECD category: Applied mechanics

In this contribution, we pay an attention on an extension of the direct inversion of mass matrix for higher-order finite element method and its application for numerical modelling in structural dynamics. In works, the following formula for the inversion of the mass matrix M has been derived based on the Hamilton's principle as follows M-1 = A-TCA-1 where M is the mass matrix, M-1 is its inversion, C is labeled as the momentum matrix, A is the diagonal projection matrix. The final form of the inverse matrix mass is sparse, symmetrical and preserving the total mass. In the first step of the approach, the inverse mass matrix for the floating system is obtained and in the second step, the Dirichlet boundary conditions are applied via the method of Localized Lagrange Multipliers [3]. In the contribution, we discuss using different lumping approaches for the A-projection matrix based on Row-summing, Diagonal scaling method, Quadrature-based lumping and Manifold-based method. We analyze accuracy of obtained inverse mass matrices in free vibration problems and their convergence rates.
Permanent Link: http://hdl.handle.net/11104/0304500