An optimal high-order non-reflecting finite element scheme for wave scattering problems

A new 1nite element scheme is proposed for the numerical solution of time-harmonic wave scattering problems in unbounded domains. The in1nite domain in truncated via an arti1cial boundary B which encloses a 1nite computational domain <. On B a local high-order non-re/ecting boundary condition (NRBC) is applied which is constructed to be optimal in a certain sense. This NRBC is implemented in a special way, by using auxiliary variables along the boundary B, so that it involves no high-order derivatives regardless of its order. The order of the scheme is simply an input parameter, and it may be arbitrarily high. This leads to a symmetric 1nite element formulation where standard C0 1nite elements are used in <. The performance of the method is demonstrated via numerical examples, and it is compared to other NRBC-based schemes. The method is shown to be highly accurate and stable, and to lead to a well-conditioned matrix problem