Trefftz Approximations: A New Framework for Nonreflecting Boundary Conditions

A new general framework for approximate nonreflecting boundary conditions in wave scattering involves a set of local Trefftz functions-outgoing waves-and a commensurate set of degrees of freedom (DOF). With specific choices of bases and DOF, one obtains classical Engquist-Majda and Bayliss-Turkel conditions. Other choices yield a variety of approximate conditions. With derivatives of the solution as additional boundary DOF, accurate results can be obtained even on fairly coarse grids, as illustrated numerically.