Mass lumping and outlier removal strategies for complex geometries in isogeometric analysis
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| Format: | Preprint |
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2024
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| _version_ | 1866916511602442240 |
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| author | Voet, Yannis Sande, Espen Buffa, Annalisa |
| author_facet | Voet, Yannis Sande, Espen Buffa, Annalisa |
| contents | Mass lumping techniques are commonly employed in explicit time integration schemes for problems in structural dynamics and both avoid solving costly linear systems with the consistent mass matrix and increase the critical time step. In isogeometric analysis, the critical time step is constrained by so-called "outlier" frequencies, representing the inaccurate high frequency part of the spectrum. Removing or dampening these high frequencies is paramount for fast explicit solution techniques. In this work, we propose mass lumping and outlier removal techniques for nontrivial geometries, including multipatch and trimmed geometries. Our lumping strategies provably do not deteriorate (and often improve) the CFL condition of the original problem and are combined with deflation techniques to remove persistent outlier frequencies. Numerical experiments reveal the advantages of the method, especially for simulations covering large time spans where they may halve the number of iterations with little or no effect on the numerical solution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_14956 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mass lumping and outlier removal strategies for complex geometries in isogeometric analysis Voet, Yannis Sande, Espen Buffa, Annalisa Numerical Analysis 65M60, 65F15 Mass lumping techniques are commonly employed in explicit time integration schemes for problems in structural dynamics and both avoid solving costly linear systems with the consistent mass matrix and increase the critical time step. In isogeometric analysis, the critical time step is constrained by so-called "outlier" frequencies, representing the inaccurate high frequency part of the spectrum. Removing or dampening these high frequencies is paramount for fast explicit solution techniques. In this work, we propose mass lumping and outlier removal techniques for nontrivial geometries, including multipatch and trimmed geometries. Our lumping strategies provably do not deteriorate (and often improve) the CFL condition of the original problem and are combined with deflation techniques to remove persistent outlier frequencies. Numerical experiments reveal the advantages of the method, especially for simulations covering large time spans where they may halve the number of iterations with little or no effect on the numerical solution. |
| title | Mass lumping and outlier removal strategies for complex geometries in isogeometric analysis |
| topic | Numerical Analysis 65M60, 65F15 |
| url | https://arxiv.org/abs/2402.14956 |