Higher order accurate mass lumping for explicit isogeometric methods based on approximate dual basis functions
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913665690632192 |
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| author | Hiemstra, Rene Nguyen, Thi-Hoa Eisentrager, Sascha Dornisch, Wolfgang Schillinger, Dominik |
| author_facet | Hiemstra, Rene Nguyen, Thi-Hoa Eisentrager, Sascha Dornisch, Wolfgang Schillinger, Dominik |
| contents | This paper introduces a mathematical framework for explicit structural dynamics, employing approximate dual functionals and rowsum mass lumping. We demonstrate that the approach may be interpreted as a Petrov-Galerkin method that utilizes rowsum mass lumping or as a Galerkin method with a customized higher-order accurate mass matrix. Unlike prior work, our method correctly incorporates Dirichlet boundary conditions while preserving higher order accuracy. The mathematical analysis is substantiated by spectral analysis and a two-dimensional linear benchmark that involves a non-linear geometric mapping. Our results reveal that our approach achieves accuracy and robustness comparable to a traditional Galerkin method employing the consistent mass formulation, while retaining the explicit nature of the lumped mass formulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_13379 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Higher order accurate mass lumping for explicit isogeometric methods based on approximate dual basis functions Hiemstra, Rene Nguyen, Thi-Hoa Eisentrager, Sascha Dornisch, Wolfgang Schillinger, Dominik Numerical Analysis 65M60, 65M12, 65L06, 65D07 This paper introduces a mathematical framework for explicit structural dynamics, employing approximate dual functionals and rowsum mass lumping. We demonstrate that the approach may be interpreted as a Petrov-Galerkin method that utilizes rowsum mass lumping or as a Galerkin method with a customized higher-order accurate mass matrix. Unlike prior work, our method correctly incorporates Dirichlet boundary conditions while preserving higher order accuracy. The mathematical analysis is substantiated by spectral analysis and a two-dimensional linear benchmark that involves a non-linear geometric mapping. Our results reveal that our approach achieves accuracy and robustness comparable to a traditional Galerkin method employing the consistent mass formulation, while retaining the explicit nature of the lumped mass formulation. |
| title | Higher order accurate mass lumping for explicit isogeometric methods based on approximate dual basis functions |
| topic | Numerical Analysis 65M60, 65M12, 65L06, 65D07 |
| url | https://arxiv.org/abs/2310.13379 |