Optimal local nonreflecting boundary conditions for time-dependent waves

Nonreflecting Boundary Conditions (NRBCs) are often used on artificial boun daries as a method for the numerical solution of wave problems in unbounded domains. Recently, a two-parameter hierarchy of optimal local NRBCs of inc reasing order has been developed for elliptic problems, including the probl em of time-harmonic acoustic waves. The optimality is in the sense that the local NRBC best approximates the exact nonlocal Dirichlet-to-Neumann (DtN) boundary condition in the L-2 norm for functions which can be Fourier-deco mposed. The optimal NRBCs are combined with finite element discretization i n the computational domain. Here this approach is extended to time-dependen t acoustic waves. In doing this, the Semi-Discrete DtN approach is used as the starting point. Numerical examples involving propagating disturbances i n two dimensions are given.