2D discrete Hodge-Dirac operator on the torus

2D discrete Hodge-Dirac operator on the torus

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...

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Veröffentlicht in:arXiv.org 2022-02
1. Verfasser: Sushch, Volodymyr
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Sprache:eng
Schlagworte:
Combinatorial analysis
Computer Science - Numerical Analysis
Homology
Mathematical analysis
Mathematics - Combinatorics
Mathematics - Differential Geometry
Mathematics - Mathematical Physics
Mathematics - Numerical Analysis
Physics - Mathematical Physics
Toruses
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description 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.
doi_str_mv 10.48550/arxiv.2202.03923
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subjects Combinatorial analysis
Computer Science - Numerical Analysis
Homology
Mathematical analysis
Mathematics - Combinatorics
Mathematics - Differential Geometry
Mathematics - Mathematical Physics
Mathematics - Numerical Analysis
Physics - Mathematical Physics
Toruses
title 2D discrete Hodge-Dirac operator on the torus
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