2D discrete Hodge-Dirac operator on the torus
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866910458313703424 |
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| author | Sushch, Volodymyr |
| author_facet | Sushch, Volodymyr |
| contents | We discuss a discretisation of the de Rham-Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge-Dirac and Laplace operators in which key geometric aspects of the continuum counterpart are captured. We provide and prove a discrete version of the Hodge decomposition theorem. Special attention has been paid to discrete models on a combinatorial torus. In this particular case, we also define and calculate the cohomology groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_03923 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | 2D discrete Hodge-Dirac operator on the torus Sushch, Volodymyr Mathematical Physics Numerical Analysis Combinatorics Differential Geometry 39A12, 39A70, 58A14 We discuss a discretisation of the de Rham-Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge-Dirac and Laplace operators in which key geometric aspects of the continuum counterpart are captured. We provide and prove a discrete version of the Hodge decomposition theorem. Special attention has been paid to discrete models on a combinatorial torus. In this particular case, we also define and calculate the cohomology groups. |
| title | 2D discrete Hodge-Dirac operator on the torus |
| topic | Mathematical Physics Numerical Analysis Combinatorics Differential Geometry 39A12, 39A70, 58A14 |
| url | https://arxiv.org/abs/2202.03923 |