Three-dimensional infinite elements for exterior problems of time-harmonic acoustics are developed. The infinite elements mesh only the outer boundary of the finite element domain and need not match the finite elements on the interface. A four-noded infinite element, based on separation of variables in spherical coordinates, is presented. Singular behavior of associated Legendre functions at the poles is circumvented. Numerical results validate the good performance of this approach.

No 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.