Dynamic solution of unbounded domains using finite element method: discrete Greenʹs functions in frequency domain

In this paper we present a new approach for finite element solution of time-harmonic wave problems on unbounded domains. As representatives of the wave problems, discrete Green’s functions are evaluated in finite element sense. The finite element mesh is considered to be of repeatable pattern (cell) constructed in rectangular co-ordinates. The system of FE equations is therefore reduced to a set of well-known dispersion equations by using a spectral solution approach. The spectral wave bases are constructed directly from the FE dispersion equations. Radiation condition is satisfied by selecting the wave bases so that the wave information is transmitted in appropriate directions at the cell level. Dirichlet/Neumann boundary conditions are defined at the edges of a quadrant of the main domain while using the axes of symmetry of the problem. A new discrete transformation method, recently proposed by the authors, is used to satisfy the boundary conditions. Comprehensive studies are made for showing the validity, accuracy and convergence of the solutions. The results of the benchmark problems indicate that the proposed method can be used to evaluate discrete Green’s functions whose analytical forms are not available. Copyright 2006 John Wiley & Sons, Ltd