Stable high-order absorbing boundary condition based on new continued fraction for scalar wave propagation in unbounded multilayer media

A long-time stable high-order absorbing boundary condition (ABC) is developed for the finite element simulation of time-dependent scalar wave propagation in unbounded multilayer media that is a multilayer waveguide. The ABC is obtained based on a new continued fraction (CF) expansion of the frequency-domain dynamic stiffness matrix on the artificial boundary of a truncated infinite domain. The dynamic stiffness in scalar CF form is first proposed in the modal space for a single-layered medium and is subsequently extended to a matrix CF form for multilayer media. The new CF converges to dynamic stiffness over the whole frequency range as its order increases for the single-layered medium, and has high accuracy for the multilayer media. The CF-based high-order ABC is therefore accurate and stable in the time domain. After being coupled seamlessly with finite element method (FEM), instability phenomena are observed during long-time computation. In order to eliminate the instability of the coupled ABC and FEM system, a straightforward and effective method is proposed by introducing damping proportional to the stiffness matrix of spatially discretised finite domain. Numerical examples demonstrate the superior properties of the proposed ABC with high accuracy and long-time stability as well as remarkable coupling with FEM.