New Approaches to High-Resolution Methods for Wave Simulation

1. University of Alabama Mathematics Box 870350 Tuscaloosa, AL 35487 (205) 348-5071 Colloquium Thomas Hagstrom Southern Methodist University November 2, 2012 3:00 pm. 346 Gordon Palmer Refreshments provided New Approaches to High-Resolution Methods for Wave Simulation Typical problems in wave theory involve multiple spatiotemporal scales, ranging from the propagation range to the wavelengths to even smallerscale features associated with scatterers or other inhomogeneities. Thus they pose a stiff challenge to numerical technique. We believe that reliable highresolutionvolume discretizations applicable in complex geometry (i.e. on grids that can be generated efficiently) are necessary to solve difficult 3 + 1- dimensional problems with the possibility of error control. In this talk we will give a critical overview of existing high-resolution discretization techniques. We go on to discuss our own work on methods which overcome some of the difficulties in existing methods. These new methods include novel spectral elements based on Hermite interpolation, the stabilization of high-order one-sided differentiation using minimal mesh grading, as well as the hybridization of structured and unstructured grids. -Thomas Hagstrom