Finite element analysis of time-dependent semi-infinite wave-guides with high-order boundary treatment

A new nite element (FE) scheme is proposed for the solution of time-dependent semi-in nite waveguide problems, in dispersive or non-dispersive media. The semi-in nite domain is truncated via an arti cial boundary B, and a high-order non-re ecting boundary condition (NRBC), based on the Higdon non-re ecting operators, is developed and applied on B. The new NRBC does not involve any high derivatives beyond second order, but its order of accuracy is as high as one desires. It involves some parameters which are chosen automatically as a pre-process. A C0 semi-discrete FE formulation incorporating this NRBC is constructed for the problem in the nite domain bounded by B. Augmented and split versions of this FE formulation are proposed. The semi-discrete system of equations is solved by the Newmark time-integration scheme. Numerical examples concerning dispersive waves in a semiin nite wave guide are used to demonstrate the performance of the new method