A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains
Author(s)
Mattos Da Silva, Leticia
Stein, Oded
Solomon, Justin
Date Issued
May 28, 2024
Journal
ACM Transactions on Graphics
Publisher
Association for Computing Machinery (ACM)
Citation
Mattos Da Silva, Leticia, Stein, Oded and Solomon, Justin. 2024. "A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains." ACM Transactions on Graphics.
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Center for Computational Science and Engineering
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/3666087
