DMS Colloquium: Professor Thomas Hagstrom

Speaker: Professor Thomas Hagstrom, Southern Methodist University (Dallas, Texas)

Title: Hermite Interpolation and Differential Equations

Abstract: An amazing property of Hermite interpolation is that it is a projection in a Sobolev seminorm. As a result, in constrast with the usual Lagrange interpolant, Hermite interpolation has a smoothing effect. We show how to exploit this projection property to develop Hermite-based solvers for differential equations with novel properties. For hyperbolic pdes, Hermite methods admit order-independent time steps and highly localized evolution processes which can be exploited on modern computer architectures. For initial value problems one can develop implicit schemes of arbitrary order for which the system size is also order-independent.

Faculty host: Junshan Lin