TRANSPARENT BOUNDARY-CONDITIONS FOR PARABOLIC EQUATION SOLUTIONS OF RADIOWAVE PROPAGATION PROBLEMS

Perfectly transparent boundary conditions are derived for truncating t he integration domain when solving radiowave propagation problems with a parabolic equation (PE) method, The boundary conditions are nonloca l: they are expressed as a convolution integral involving the field at all previous ranges. The convolution kernel is matched to the refract ive index vertical gradient at the boundary. The boundary conditions i nclude an incoming energy term which can model an arbitrary incident f ield, In particular, they may be used with plane-wave incidence, or wi th a point-source located below or above the domain boundary, If requi red, the solution can be extended to heights above the boundary with a generalized horizontal PE method. Closed-form solutions for the incom ing energy term are given for plane-wave incidence and for Gaussian so urces when the refractive index above the boundary is constant or line ar, The resulting finite-difference algorithms provide efficient solut ions to problems involving airborne sources, Numerical examples are gi ven, showing excellent agreement with a pure split-step/Fourier PE alg orithm.