Numerical and spectral investigations of trefftz infinite elements

The numerical and spectral performance of novel infinite elements for exterior problems of time-harmonic acoustics are examined. The formulation is based on a functional which provides a general framework for domain-based computation of exterior problems. Two prominent features simplify the task of discretization: the infinite elements mesh the interface only and need not match the finite elements on the interface. Various infinite element approximations for two-dimensional configurations with circular interfaces are reviewed. Numerical results demonstrate the good performance of these schemes. A simple study points to the proper interpretation of spectral results for the formulation. The spectral properties of these infinite elements are examined with a view to the representation of physics and efficient numerical solution.