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We propose a novel technique to compute response gradients (Jacobians) from frequency-domain field solutions provided by high-frequency electromagnetic (EM) simulations. It is based on our recently developed self-adjoint sensitivityanalysis (SASA) approach where only one EM simulation suffices to obtain both the responses and their gradients in the optimizable-parameter space. Our novel technique exploits the computational efficiency of the SASA while adapting it to the system equations of the frequency-domain finite-difference (FDFD) method. There are three major advantages to this development: (a) the Jacobian computation is completely independent of the simulation engine, its grid and its system equations; (b) the implementation is straightforward and in the form of a post-processing algorithm operating on the exported field solution; (c) it is computationally very efficient-memory and computer-time requirements are negligible compared to those of the simulation itself. The proposed technique drastically reduces the overall time required by field-based optimization processes arising in design and inverse problems as compared to response Jacobians computed via response-level finite differences or parameter sweeps. Its accuracy is verified by comparisons with response-level central finite-difference derivative estimates.Index Terms -Sensitivity analysis, finite-difference frequency-domain method, finite-element method .

We propose a sensitivity solver for frequencydomain analysis engines based on volume methods such as the finite-element method. Our sensitivity solver computes Sparameter 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.Index Terms -Sensitivity analysis, response Jacobians, gradient-based optimization, computer-aided design, finitedifference method, finite-element method, filter design.978-1-4244-1780-3/08/$25.00

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