Solving partial differential equations (PDEs) on curved surfaces is
important in many areas of science. The Closest Point Method is a new
technique for computing numerical solutions to PDEs on curves,
surfaces, and more general domains. For example, it can be used to
solve a pattern-formation PDE on the surface of a rabbit.
A benefit of the Closest Point Method is its simplicity: it is easy to
understand and straightforward to implement on a wide variety of PDEs
and surfaces. In this presentation, I will introduce the Closest
Point Method and highlight some of the research in this area. Example
computations (including the in-surface heat equation,
reaction-diffusion on surfaces, level set equations, high-order
interface motion, and Laplace--Beltrami eigenmodes) on a variety of
surfaces will demonstrate the effectiveness of the method.