A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
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| _version_ | 1866916270245412864 |
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| author | Da Silva, Leticia Mattos Stein, Oded Solomon, Justin |
| author_facet | Da Silva, Leticia Mattos Stein, Oded Solomon, Justin |
| contents | We introduce a framework for solving a class of parabolic partial differential equations on triangle mesh surfaces, including the Hamilton-Jacobi equation and the Fokker-Planck equation. PDE in this class often have nonlinear or stiff terms that cannot be resolved with standard methods on curved triangle meshes. To address this challenge, we leverage a splitting integrator combined with a convex optimization step to solve these PDE. Our machinery can be used to compute entropic approximation of optimal transport distances on geometric domains, overcoming the numerical limitations of the state-of-the-art method. In addition, we demonstrate the versatility of our method on a number of linear and nonlinear PDE that appear in diffusion and front propagation tasks in geometry processing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00327 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains Da Silva, Leticia Mattos Stein, Oded Solomon, Justin Numerical Analysis Graphics We introduce a framework for solving a class of parabolic partial differential equations on triangle mesh surfaces, including the Hamilton-Jacobi equation and the Fokker-Planck equation. PDE in this class often have nonlinear or stiff terms that cannot be resolved with standard methods on curved triangle meshes. To address this challenge, we leverage a splitting integrator combined with a convex optimization step to solve these PDE. Our machinery can be used to compute entropic approximation of optimal transport distances on geometric domains, overcoming the numerical limitations of the state-of-the-art method. In addition, we demonstrate the versatility of our method on a number of linear and nonlinear PDE that appear in diffusion and front propagation tasks in geometry processing. |
| title | A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains |
| topic | Numerical Analysis Graphics |
| url | https://arxiv.org/abs/2312.00327 |