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

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Result language
angličtina
Original language name
Inverse mass matrix for higher-order finite element method via localized Lagrange multipliers
Original language description
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.
Czech name
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Czech description
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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