Stable and accurate outgoing wave filters for anisotropic and nonlocal waves

The Perfectly Matched Layer (PML) is currently the mainstay of absorbing boundary conditions. For some anisotropic wave equations the PML is exponentially unstable in time. We present in this work a new method of open boundaries, the phase space filter, which is stable for all wave equations. Outgoing waves can be are waves located near the boundary of the computational domain with group velocities pointing out. Phase space filtering involves periodically removing only outgoing waves from the solution, leaving non-outgoing waves unchanged. We apply this method to the Euler equations (linearized about a jet ow), Maxwell equations in a birefringent medium and the quasi-geostrophic equations.