Speaker: David Ketcheson, Applied Mathematics
Title:
Time: 3:30 PM, Thursday, 11/18/04
Place: Guggenheim Room 408d
Abstract:
The commonly used method of lines or semi-discretization technique for approximating solutions to PDEs results in a system of ODEs that must be integrated in time. Often the semi-discrete scheme is designed to satisfy desirable bounds under forward Euler integration. Strong Stability Preserving (SSP) time integrators yield a solution satisfying the same bounds while achieving higher order temporal accuracy, even for nonlinear PDEs and bounds in arbitrary norms.
I will review previous results on SSP methods and then present my own work, which has linked the SSP property for Runge-Kutta (RK) methods to the well-developed theory of absolutely monotonic RK methods. This result allows a more direct characterization of SSP RK methods and thus simplifies the search for optimal methods. It also allows a host of results from the ODE literature to be applied to SSP methods for PDEs. I will illustrate the practical value of this discovery by presenting new optimal implicit and diagonally split SSP RK methods, with results of their application to simple nonlinear and non-autonomous hyperbolic PDEs.
Everyone welcome!