UBC Mathematical Biology Seminar: Steven Ruuth

The closest point method (CPM) is a numerical method that was originally developed to solve partial differential equations (PDEs) on smooth, static surfaces using standard finite difference and interpolation methods. In this talk, we describe a recent generalization of the CPM to evolving surfaces. In our approach, the desired surface motion is obtained by evolving the underlying surface representation via the grid based particle method. We present a number of examples to illustrate the numerical convergence properties of our proposed method. Experiments for reaction-diffusion, advection-diffusion and Cahn-Hilliard equations that are strongly coupled to the velocity of the surface are also presented.