Absorbing Boundary Conditions for Adjoint Problems in the Design Sensitivity Analysis With the FDTD Method

In this paper, absorbing boundary conditions (ABCs) for adjoint problems with a backward time variable are derived from first principles. It is shown that all single-layer ABCs for the adjoint backward time problem, which are based on the one-way wave equation, have the same form as for the original forward time problem. In the case of the adjoint perfectly matched layer (PML) ABC, the signs before the spatial derivatives are opposite to those …