Central-Node Approach for Accurate Self-Adjoint Sensitivity Analysis of Dielectric Structures

The field solution at the perturbation grid points is needed to perform sensitivity analysis using adjoint approaches. On the other hand, the field solutions provided by time-domain solvers are the least accurate at dielectric interfaces, especially in the case of significant losses. These interfaces are the places where some or all perturbation grid points reside. We propose a central-node approach for the case of dielectric mediums with or without loss. The accuracy of this approach is one order higher than that of our original adjoint approach in the case of dielectric discontinuities, while the computational efficiency remains the same. Verification is carried out through examples using commercial finite-difference time-domain solvers.