Trustworthy Electromagnetic Computation for Non-Penetrable Targets Using Integral Equations

With the increasing maturity of various computational electromagnetics algorithms, the field has evolved from traditional standalone electromagnetic simulations to a stage in which trustworthy electromagnetic computation methods serve as the core, aimed at meeting the advanced demands of computer-aided engineering. Trustworthy electromagnetic computation consists of three key aspects: trustworthy model, trustworthy mesh, and trustworthy algorithm. This paper focuses on the aspect of trustworthy mesh, aiming to establish a systematic framework and methodology for achieving trustworthy computation under the assumption that the target geometry and associated parameters are determined. The framework starts with high-fidelity geometric meshing. An effective strategy is nonconformal domain decomposition, which facilitates accurate modeling of complex geometries and diverse materials. Subsequently, efficient preconditioning methods are utilized to ensure stable convergence when solving the resulting multiscale systems associated with high-fidelity meshes. After obtaining the numerical solution, verification procedures are applied to evaluate whether the desired accuracy has been achieved. If the solution fails to meet the specified precision, adaptive mesh refinement techniques are used to automatically redistribute mesh density. The objective is to attain greater accuracy with a minimal increase in degrees of freedom, thereby enhancing computational efficiency. The adaptive refinement process proceeds iteratively until the computed solution satisfies the established accuracy criteria. Within this framework, we propose a novel, fast, physics-based self-reference method, which leverages power conservation laws to assess the accuracy of the solution.