Effective methods for high frequency Helmholtz equation beyond geometrical optics

：罗松挺副教授
：2020-01-06 10:00
：数理大楼661

       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：数理大楼661

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.

 Speaker  Introduction：Dr. Songting Luo is an Associate Professor in the Department of Mathematics at Iowa State University. He received PhD degree from University of California, Irvine in 2009. Before joining Iowa State University in 2012, he was a visiting Assistant Professor at Michigan State University.  His research mainly focuses on applied computational mathematics, especially on computational high frequency wave propagation, multi-physics modeling multi-scale computation of nano optics, efficient methods for static Hamilton-Jacobi equations.

 

 

 联系人：熊涛教授