A Simple Technique for Solving Partial Differential Equations on Surfaces

  • Date: 01/19/2007

Steve Ruuth (Simon Fraser University)


Simon Fraser University


Many applications require the solution of time dependent partial
differential equations (PDEs) on surfaces or more general manifolds.
Methods for treating such problems include surface parameterization,
methods on triangulated surfaces and embedding techniques. In
particular, embedding techniques using level set representations have
received recent attention due to their simplicity. Level set based
methods have several limitations, however. These include the inability
to naturally treat open surfaces or objects of codimension two or
higher. Level set methods also typically lead to a degradation in the
order of accuracy when solved on a banded grid.

This talk describes an approach based on the closest point
representation of the surface which eliminates these and other
limitations. A noteworthy feature of the method is that it is
remarkably simple, requiring only minimal changes to the corresponding
three-dimensional codes to treat the evolution of partial differential
equations on surfaces.

Other Information: 

Centre for Scientific Computing Seminar 2007