A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains
Name
mattosdasilva-leticiam-sm-eecs-2023-thesis.pdf
Description
Thesis PDF
Size
46.8 MB
Format
Adobe PDF
Checksum (MD5)
e705c76500f4af975ae838aa61b3c0b3
Author(s)
Mattos Da Silva, Leticia
Advisor(s)
Solomon, Justin
Date Issued
June 2023
Publisher
Massachusetts Institute of Technology
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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