Speaker: Chris Stolk (UvA)
Title: Recent results on the discretization and solution of time harmonic wave equations
Abstract: Time-harmonic wave equations, acoustic or electromagnetic, have many applications, e.g. in seismology and scattering theory. In this talk we consider the Helmholtz equation for time-harmonic acoustic waves in the high-frequency limit, i.e. in the case of waves propagating over long distances. We present a new finite difference discretization, based on Fourier analysis and geometrical optics. It yields accurate simulation results using very few grid points per wave length, in case the medium varies smoothly. By using it within a multigrid method, possibly combined with domain decomposition, more general Helmholtz problems can be efficiently solved.
