A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains
Leticia Mattos Da Silva,
Oded Stein,
Justin Solomon
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 transpo… Show more
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