Computational Mathematics Seminar - Graham Mauer

Graham Mauer, Department of Applied Mathematics, University of Colorado Boulder

A Direct FEM-BIE Coupling for Free-Space Helmholtz Scattering

Free space scattering problems involving locally compact, non-homogeneous media arise in a variety of applications including medical imaging, seismology, and acoustics. These problems are challenging because it is impossible to discretize all of space. Conventional solution methods, such as absorbing boundary conditions and perfectly matched layers, truncate the domain but sometimes give rise to artificial reflections especially as the frequency grows. We propose a finite element (FEM) -based technique that utilizes integral equations to naturally satisfy the radiation condition and mitigate such reflections. The technique is a modernized FEM-BEM coupling scheme. An artificial boundary is introduced that contains the support of the variable media. In that region, a FEM is employed and a Dirichlet-to-Neumann operator is constructed. This operator is used to glue the free-space with the interior via a well-conditioned integral operator. An additional advantage of this technique is that the discretizations of both the integral equation and the FEM only need to be constructed once, independent of the number of incident waves. Numerical results will illustrate the performance of the solution technique.