The Implicit Closest Point Method for the Numerical Solution of Partial Differential Equations on Surfaces

In this presentation, we describe an implicit Closest Point Method [3] which allows large, stable time steps for high-order PDEs while retaining the principal benefits of the original method. Example computations (including the in-surface heat equation, reaction-diffusion on surfaces, Laplace–Beltrami eigenmodes, and fourth-order interface motion) on a variety of surfaces demonstrate the effectiveness of the method.