Efficient Numerical Implementation of Discrete Transparent Boundary Conditions for Parabolic Equations in Underwater Acoustics

This paper is concerned with transparent boundary conditions (TBCs) for wide angle parabolic equations (WAPEs) in the application to underwater acoustics. In a previous work a discrete TBC of convolution type was derived from the fully discretized whole-space problem that is reflection-free and yields an unconditionally stable scheme. However, since the perfect discrete TBC for the WAPE is non-local in range, its numerical evaluation becomes very costly for large-range simulations. As a remedy we construct new approximate TBCs in the form of a discrete sum-of-exponentials, which can be evaluated in a very efficient recursion.