Accurate H‐shaped absorbing boundary condition in frequency domain for scalar wave propagation in layered half‐space

Abstract

AbstractAn accurate absorbing boundary condition (ABC) is developed in frequency domain for finite element analysis of scalar wave propagation in unbounded layered half‐space. The proposed ABC is H‐shaped line that consists of two parts: a new ABC at horizontal bottom boundary of finite domain to replace semiinfinite strip below horizontal boundary and between two vertical boundaries, and a general consistent ABC at vertical lateral boundary to replace semiinfinite layered half‐space outside vertical boundary. The key point for constructing the ABC is that a new continued fraction (CF) is presented to expand dynamic stiffness of underlying half‐space, and the CF‐based stress‐displacement relationship is then transformed into an auxiliary variable system with square of horizontal wavenumber. The ABC has only one undetermined real parameter that is the CF‐order independent of frequency and incidence angle of propagating outgoing waves. The parameter can be chosen relatively small value to achieve an accurate ABC. Moreover, the ABC can couple seamlessly with finite element method of finite domain. The finite domain can be chosen very small size due to high accuracy of the ABC. Numerical examples are finally given to demonstrate the effectiveness of the ABC.