Hodge-Dirac wave systems and structure-preserving discretizations of the linearized Einstein equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911284302184448 |
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| author | Hanot, Marien-Lorenzo Hu, Kaibo |
| author_facet | Hanot, Marien-Lorenzo Hu, Kaibo |
| contents | We derive a reformulation of the linearized Arnowitt-Deser-Misner (ADM) equations as a Hodge-Dirac wave system with the divdiv complex, addressing challenges in numerical relativity such as gauge fixing, constraint propagation, and tensor symmetries. The differential and algebraic structures of the divdiv complex ensure the well-posedness of the formulation and facilitate structure-preserving discretization via finite element exterior calculus. We establish the well-posedness of this Hodge-Dirac wave equation and develop a discretization scheme applicable to both conforming and non-conforming discrete complexes, deriving error estimates under minimal assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19441 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hodge-Dirac wave systems and structure-preserving discretizations of the linearized Einstein equations Hanot, Marien-Lorenzo Hu, Kaibo General Relativity and Quantum Cosmology Numerical Analysis 65M12, 65N30, 65M60, 83C27 We derive a reformulation of the linearized Arnowitt-Deser-Misner (ADM) equations as a Hodge-Dirac wave system with the divdiv complex, addressing challenges in numerical relativity such as gauge fixing, constraint propagation, and tensor symmetries. The differential and algebraic structures of the divdiv complex ensure the well-posedness of the formulation and facilitate structure-preserving discretization via finite element exterior calculus. We establish the well-posedness of this Hodge-Dirac wave equation and develop a discretization scheme applicable to both conforming and non-conforming discrete complexes, deriving error estimates under minimal assumptions. |
| title | Hodge-Dirac wave systems and structure-preserving discretizations of the linearized Einstein equations |
| topic | General Relativity and Quantum Cosmology Numerical Analysis 65M12, 65N30, 65M60, 83C27 |
| url | https://arxiv.org/abs/2511.19441 |