2026-09-19T22:59:12Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1515672023-08-01T03:21:55Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Solomon, Justin
Mattos Da Silva, Leticia
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2023-07-31T19:49:09Z
2023-07-31T19:49:09Z
2023-06
2023-07-13T14:24:44.197Z
https://hdl.handle.net/1721.1/151567
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. Certain PDE in this class often have nonlinear or stiff terms that cannot be resolved with standard methods on triangle mesh surfaces. 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 tasks in geometry processing.
S.M.
Massachusetts Institute of Technology
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A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains
Thesis
application/pdf
Master
Master of Science in Electrical Engineering and Computer Science
Publication
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<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. Certain PDE in this class often have nonlinear or stiff terms that cannot be resolved with standard methods on triangle mesh surfaces. 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 tasks in geometry processing.</Abstract>
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