Colin B. Macdonald
Department of Mathematics
Simon Fraser University
The Closest Point Method is a recent technique for computing motion on surfaces embedded in 3D. For example, the Closest Point Method could be used to compute a numerical solution of a partial differential equation on the surface of sphere, torus or Mobius strip.
In this presentation, we will introduce the Closest Point Method and describe some of its advantages over other embedding methods. We will then present some current research on the Closest Point Method applied to the motion of interfaces governed by Level Set equations on surfaces. Several numerical examples, including flow on triangulated surfaces and flow on a 4D Klein bottle, demonstrate that the method is both highly accurate and very flexible with respect to the geometry of the surface.
This is joint work with Steven J. Ruuth (Simon Fraser University).