Please note: This PhD seminar will be given online.
Nathan
King, PhD
candidate
David
R.
Cheriton
School
of
Computer
Science
Supervisor: Professor Christopher Batty
Partial differential equations (PDEs) posed on surfaces are found in many fields such as biological systems, fluid dynamics, computer graphics, image processing, and medical imaging. The closest point method is a numerical framework that embeds the surface problem in the surrounding Euclidean space to give a Cartesian analog of the PDE. This enables the use of standard Cartesian numerical methods, while handling general manifolds that are open or closed, with or without orientation, and of mixed co-dimension.
This talk will give an overview of this simple embedding numerical method for solving surface PDEs. It is shown that the closest point method can be applied to general classes of surface PDEs, including advection, diffusion, reaction-diffusion, eigenvalue problems, and surface mapping. Handling problems with Dirichlet constraints on the interior of the surface arises in multiple applications of PDEs, including geodesic distance computation. An approach to incorporating surface interior constraints with the closest point method is explored.
To join this PhD seminar on MS Teams, please go to https://teams.microsoft.com/l/meetup-join/19%3ameeting_ZGMxOTk4MGMtOGUzNC00MTVjLWI4NjQtOGM1ZTAxYzFiZWVm%40thread.v2/0?context=%7b%22Tid%22%3a%22723a5a87-f39a-4a22-9247-3fc240c01396%22%2c%22Oid%22%3a%2292c3e79f-540a-4d0b-a83d-a85edd23280e%22%7d.