Unconditionally stable space-time isogeometric discretization for the wave equation in Hamiltonian formulation
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909374620893184 |
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| author | Ferrari, Matteo Fraschini, Sara Loli, Gabriele Perugia, Ilaria |
| author_facet | Ferrari, Matteo Fraschini, Sara Loli, Gabriele Perugia, Ilaria |
| contents | We consider a family of conforming space-time discretizations for the wave equation based on a first-order-in-time formulation employing maximal regularity splines. In contrast with second-order-in-time formulations, which require a CFL condition to guarantee stability, the methods we consider here are unconditionally stable without the need for stabilization terms. Along the lines of the work by M. Ferrari and S. Fraschini (2024), we address the stability analysis by studying the properties of the condition number of a family of matrices associated with the time discretization. Numerical tests validate the performance of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00650 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unconditionally stable space-time isogeometric discretization for the wave equation in Hamiltonian formulation Ferrari, Matteo Fraschini, Sara Loli, Gabriele Perugia, Ilaria Numerical Analysis 65M60, 15A12, 65L60, 15B05 We consider a family of conforming space-time discretizations for the wave equation based on a first-order-in-time formulation employing maximal regularity splines. In contrast with second-order-in-time formulations, which require a CFL condition to guarantee stability, the methods we consider here are unconditionally stable without the need for stabilization terms. Along the lines of the work by M. Ferrari and S. Fraschini (2024), we address the stability analysis by studying the properties of the condition number of a family of matrices associated with the time discretization. Numerical tests validate the performance of the method. |
| title | Unconditionally stable space-time isogeometric discretization for the wave equation in Hamiltonian formulation |
| topic | Numerical Analysis 65M60, 15A12, 65L60, 15B05 |
| url | https://arxiv.org/abs/2411.00650 |