Adjoint-Based Accelerated Adaptive Refinement in Frequency Domain 3-D Finite Element Method Scattering Problems

We present the application of adjoint analysis to 3-D finite-element method scattering problems for a posteriori error estimation and adaptive refinement. Adjoint-based methodologies, though underutilized in computational electromagnetics (CEM), enable significant improvements for both efficiency and accuracy. We first formulate the adjoint problem of the 3-D double-curl wave equation and the error estimates for the construction of novel accelerated adaptive refinement algorithms. We demonstrate adaptive error control for a customizable quantity of interest (QoI) resulting in targeted refinement and improved resource allocation through the application of automatic global and local error tolerance heuristics that accelerate the refinement process. The proposed refinement algorithms rapidly refine even extremely coarse initial discretizations to high accuracy, eliminating or substantially reducing manual intervention in the generation of computationally efficient and accurate simulations. Moreover, comparisons with analytical results validate our approach to accelerating automatic refinement to fine tolerances.