Numerical and spectral investigations of Trefftz infinite elements

The numerical and spectral performance of novel in nite 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 in nite elements mesh the interface only and need not match the nite elements on the interface. Vari- ous in nite element approximations for two-dimensional con gurations 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 in nite elements are examined with a view to the representation of physics and e cient numerical solution. Copyright ? 1999 John Wiley & Sons, Ltd.