PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Fei Wang.

Title:An efficient spectral method for scattering in unbounded rough surfaces and a fast structured direct spectral solver for PDEs with variable coefficients
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Jie Shen, Purdue University
Abstract Link:
The talk will consist of two parts. In the first part, I shall present an efficient and stable spectral algorithm for solving the unbounded rough surface scattering problem, which is referred to as a non-local perturbation of an infinite plane surface such that the whole surface lies within a finite distance of the original plane. The method uses a transformed field expansion to reduce the boundary value problem with a complex scattering surface into a successive sequence of transmission problems of the Helmholtz equation with a plane surface. We then construct a special algorithm using Hermit functions to fully decouple the problem into a sequence of one-dimensional two-point boundary value problems with piecewise constant wavenumbers, which can be solved efficiently by a spectral-element method. I shall present ample numerical results to shaw that the new spectral method is efficient, accurate, and well suited to solve the scattering problem by unbounded rough surfaces. In the second part, I shall present a fast structured direct spectral solver for PDEs with variable coefficients. It is well-known that spectral methods for PDEs with variable coefficients lead to dense matrices. We shall show that the off-diagonal blocks of these dense matrices are of low-rank, so they can be solved with nearly linear complexity by a direct matrix-free solver based on the hierarchically semi-separable (HSS) representation.

Room Reservation Information

Room Number:MB106
Date:10 / 16 / 2013
Time:03:30pm - 04:30pm