Symmetric Local Absorbing Boundaries in Time and Space

Abstract

This paper is concerned with the development of simple, yet accurate, absorbing boundaries that can be incorporated readily into existing finite element programs directly in the time domain. The wave equation in a two‐dimensional exterior domain is considered as a prototype situation. For this problem a family of approximate absorbing boundary elements is constructed by an asymptotic expansion procedure. Each element is completely determined by a pair of local, symmetric, stiffnesslike and dampinglike constant matrices, coupled only through adjoining nodes. This makes it possible to combine the new boundary elements with standard finite elements used to represent the interior domain via ordinary assembly procedures, while preserving the symmetry and bandwidth of the global matrices. Results of numerical experiments for a circular geometry confirm that accuracy increases with the order of the approximations, with the radius of the absorbing boundary, and with the dominant frequencies of the excitation. This implies that the higher the frequency of the excitation the smaller the size of the buffer annulus required to attain a desired accuracy.