Plane wave discontinuous Galerkin methods for acoustic scattering
Date
2016
Authors
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Publisher
University of Delaware
Abstract
We apply the Plane Wave Discontinuous Galerkin (PWDG) method to study the direct scattering of acoustic waves from impenetrable obstacles. In the first part of the thesis we consider the full exterior scattering problem with smooth boundaries. This problem is modeled by the Helmholtz equation in the unbounded domain exterior to the scatterer. To compute the scattered field, an artificial boundary is introduced to reduce the infinite domain to a finite computational domain. We then apply Dirichlet-to-Neumann (DtN) and Neumann-to-Dirichlet (NtD) boundary conditions on a circular artificial boundary. By using asymptotic properties of Hankel functions, we are able to prove wavenumber explicit L2-norm error estimates for the DtN-PWDG method on quasi-uniform meshes. Numerical experiments indicate that the accuracy of the PWDG method for the scattering problem is improved by the use of DtN and NtD boundary conditions. The second part of the thesis concerns acoustic scattering from domains with corners. In such domains, quasi-uniform meshes are not efficient so we derive error indicators to drive the selective refinement of the mesh in an adaptive algorithm. We prove a posteriori L2-norm error estimates for the Helmholtz equation with impedance boundary conditions on the artificial boundary. Numerical results demonstrate the efficiency of the proposed indicators. This adaptive strategy is compatible with the DtN and NtD truncation of the infinite domain problem and the combination would significantly improve the accuracy and reliability of PWDG simulations.