Speaker： Dr. Songting Luo

                       Iowa State University

Title:    Effective methods for high frequency Helmholtz equation beyond geometrical optics

 Time：06 Jan 2020, 10:00

Location：Conference Room 661 at the 6th floor of Shuli Building at Haiyun Campus

Abstract:    The main difficulty for solving high frequency Helmholtz equation is that its solution is highly oscillatory. Conventional methods such as the finite difference finite element method usually suffer from high degrees of freedom to avoid the ‘pollution effects’ (large dispersion error). Geometrical optics (GO) provides an alternative way to approximate the wave, where its phase amplitude are assumed to be frequency independent, hence can be computed efficiently used to reconstruct the wave for any high frequencies. The GO approximation is in principle efficient but only valid locally. To obtain globally valid wave, we will transfer the problem to an appropriate time-dependent Schrodinger equation, propagate the wave function to the steady state through an unconditionally stable time propagator, which results in the solution to the Helmholtz equation.  Detailed formulation numerical procedure will be explained, along with numerical experiments to demonstrate the effectiveness of the proposed method.