Abstract: Solving heat diffusion problems in complicated geometries such as stellarators a typically requires using a highly refined mesh. In this work, we explore an alternative approach which uses mesh-free Monte Carlo methods to solve elliptic partial differential equations (PDEs) using a method known as Walk on Spheres. In particular, we focus on spatially varying, isotropic diffusion in Laplace's equation, discuss the connection to Brownian Motion, and motivate the algorithm’s ability to handle complex geometries without a mesh. We develop a novel variance reduction strategy, demonstrate its performance on smaller problems, and gesture towards extensions of Walk on Spheres to more complex PDEs that can handle source terms, anisotropic diffusion, etc.
(Video recording of talk)

Talk time in other timezones:
AEST   12:00 AM Fri 19 Jul,
JST    11:00 PM Thu 18 Jul,
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BST     3:00 PM Thu 18 Jul,
UTC    14:00    Thu 18 Jul,
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MST/PDT 7:00 AM Thu 18 Jul