DMS Applied Mathematics Seminar

Speaker: Professor Andrew Christlieb (Department Chair, Department of Computational Mathematics, Science and Engineering, Michigan State University)

Title: Kernel based methods as a path to Explicit unconditionally stable O(N) methods

Abstract:  In this talk we introduce the idea of a kernel based derivative.  The kernel based approach expresses a differential operator in terms of a convolution integral.  High order is achieved through successive convolution.  The approach can be paired with both explicit multi stage or explicit multi step methods.  The approach does not involve iteration, but rather it is a direct update.  The method is provably O(N) and Von Neumann analysis shows that the method is unconditionally stable for linear problems.  For non-linear problems, the method behaves unconditionally stable, but we have not proven it thus far.  We have developed these methods for the Wave equations, Hamilton Jacobi equations, Degenerate Advection Diffusion equations, as well as developed a domain decomposition approach that lets us scale these new methods to large distributed heterogeneous computers.  Further, we have extended these ideas to mapped grids.   In this talk, we will introduce the ideas in the context of the Hamilton Jacobi equations and introduce our approach for addressing complex geometry.

Join the Zoom meeting from PC, Mac, Linux, iOS or Android: https://auburn.zoom.us/j/93435983967