A boundary condition in Padé series for frequency-domain solution of wave propagation in unbounded domains

A boundary condition satisfying the radiation condition at infinity is frequently required in the numerical simulation of wave propagation in an unbounded domain. In a frequency domain analysis using finite elements, this boundary condition can be represented by the dynamic stiffness matrix of the unbounded domain defined on its boundary. A method for determining a Pad´e series of the dynamic stiffness matrix is proposed in this paper. This method starts from the scaled boundary finite-element equation, which is a system of ordinary differential equations obtained by discretizing the boundary only. The coefficients of the Pad´e series are obtained directly from the ordinary differential equations, which are not actually solved for the dynamic stiffness matrix. The high rate of convergence of the Pad´e series with increasing order is demonstrated numerically. This technique is applicable to scalar waves and elastic vector waves propagating in anisotropic unbounded domains of irregular geometry. It can be combined seamlessly with standard finite elements. Copyright q 2006 John Wiley & Sons, Ltd