SBP-FDEC: Summation-by-Parts Finite Difference Exterior Calculus
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916048334225408 |
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| author | Bach, Daniel Rueda-Ramírez, Andrés M. Sonnendrücker, Eric Fernández, David C. Del Rey Gassner, Gregor J. |
| author_facet | Bach, Daniel Rueda-Ramírez, Andrés M. Sonnendrücker, Eric Fernández, David C. Del Rey Gassner, Gregor J. |
| contents | We demonstrate that we can carry over the strategy of Finite Element Exterior Calculus (FEEC) to Summation-by-Parts (SBP) Finite Difference (FD) methods to achieve divergence- and curl-free discretizations. This is not obvious at first sight, as for SBP-FD no basis functions are known, but only values and derivatives at points. The key is a remarkable analytic relationship that enables us to construct compatible operators using integral and nodal degrees of freedom. Pre-existing SBP-FD matrix operators can then be used to obtain nodal values from the integral degrees of freedom to derive a scheme with the desired properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20529 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SBP-FDEC: Summation-by-Parts Finite Difference Exterior Calculus Bach, Daniel Rueda-Ramírez, Andrés M. Sonnendrücker, Eric Fernández, David C. Del Rey Gassner, Gregor J. Numerical Analysis 65M06, 65M20 We demonstrate that we can carry over the strategy of Finite Element Exterior Calculus (FEEC) to Summation-by-Parts (SBP) Finite Difference (FD) methods to achieve divergence- and curl-free discretizations. This is not obvious at first sight, as for SBP-FD no basis functions are known, but only values and derivatives at points. The key is a remarkable analytic relationship that enables us to construct compatible operators using integral and nodal degrees of freedom. Pre-existing SBP-FD matrix operators can then be used to obtain nodal values from the integral degrees of freedom to derive a scheme with the desired properties. |
| title | SBP-FDEC: Summation-by-Parts Finite Difference Exterior Calculus |
| topic | Numerical Analysis 65M06, 65M20 |
| url | https://arxiv.org/abs/2511.20529 |