Efficient electromagnetic optimization using self-adjoint jacobian computation based on a central-node FDFD method

We propose a sensitivity solver for frequency-domain analysis engines based on volume methods such as the finite-element method. Our sensitivity solver computes S-parameter Jacobians directly from the field solution available from the electromagnetic simulation. The computational overhead is a fraction of that of the simulation itself. It is independent from the simulator's grid, system equations and discretization method. It uses its own finite-difference grid and a sensitivity formula based on the frequency-domain finite-difference (FDFD) equation for the electric field. It computes the S-parameter gradients in the design parameter space through a self-adjoint formulation which eliminates adjoint system analyses and greatly simplifies implementation. We use our sensitivity solver in gradient-based optimization of filters. We achieve drastic reduction of the time required by the overall optimization process. All examples use a commercial finite-element simulator.