Numerical and spectral investigations of Trefftz infinite elements

Abstract

SUMMARYThe numerical and spectral performance of novel inÿnite 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 inÿnite elements mesh the interface only and need not match the ÿnite elements on the interface. Various inÿnite element approximations for two-dimensional conÿgurations 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 inÿnite elements are examined with a view to the representation of physics and e cient numerical solution.

Analytical study of the effect of wave number on the performance of local absorbing boundary conditions for acoustic scattering

“…Correct far-field behavior is then enforced either by specifying proper boundary conditions on this boundary, or by assuming interpolation with suitable behavior in the complement of the computational domain [1]. The latter approach is associated with 'infinite elements' [2][3][4][5][6]. On the other hand, artificial boundary conditions (ABC) refer to a class of methods that is based on specifying proper boundary conditions on the artificial boundary.…”