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Inverse mass matrix for higher-order finite element method via localized Lagrange multipliers
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SYSNO ASEP 0518643 Document Type A - Abstract R&D Document Type O - Ostatní Title Inverse mass matrix for higher-order finite element method via localized Lagrange multipliers Author(s) Kolman, Radek (UT-L) RID
González, J.A. (ES)
Kopačka, Ján (UT-L) RID, ORCID
Cho, S.S. (KR)
Park, K.C. (US)Number of authors 5 Source Title Modelling 2019, Book of absracts. - Ostrava : Institute of Geonics of the Czech Academy of Sciences, 2019 / Blaheta R. ; Starý J. ; Sysala S. - ISBN 978-80-86407-79-1
S. 139-140Number of pages 2 s. Publication form Print - P Action Modelling 2019: International conference on mathematical modelling and computational methods in applied sciences and engineering Event date 16.09.2019 - 20.09.2019 VEvent location Olomouc Country CZ - Czech Republic Event type WRD Language eng - English Country CZ - Czech Republic Keywords direct inversion of mass matrix ; finite element method ; free-vibration problem Subject RIV BI - Acoustics OECD category Applied mechanics R&D Projects GA19-04956S GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) EF15_003/0000493 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) Institutional support UT-L - RVO:61388998 Annotation 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. Workplace Institute of Thermomechanics Contact Marie Kajprová, kajprova@it.cas.cz, Tel.: 266 053 154 ; Jana Lahovská, jaja@it.cas.cz, Tel.: 266 053 823 Year of Publishing 2020
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