Curvilinear Nonconformal Adaptive h-Refinement Using Augmented EFIE With a Multiresolution Preconditioner for Analyzing Complex Objects

The article proposes a multiresolution preconditioned augmented electric-field integral equation (MR-AEFIE) suitable for adaptive
h
-refinement based on residual error estimation to analyze the radiation and scattering from complex objects. By enforcing the normal boundary condition of perfect conductor, the MR-AEFIE eliminates spurious internal resonances, which cause MR-EFIE to produce a spurious solution and prevent the residual-based error estimator from obtaining the correct error. Besides, the MR-AEFIE is well-conditioned and can maintain a stable number of iterations to achieve convergence during the adaptive refinement process. Moreover, the proposed MR preconditioner is curvilinear nonconformal mesh-based, which is well embedded in the framework of adaptive mesh refinement with better geometry approximation. The adaptive
h
-refinement is achieved through a nonconformal sub-meshing technique, involving the definition of multibranch curvilinear Rao–Wilton–Glisson (MB-CRWG) basis functions. Numerical results show the resonant-free attribute, high precision, and rapid convergence of the MR-AEFIE. Also, the adaptive mesh refinement based on MR-AEFIE is demonstrated to achieve higher accuracy with fewer unknowns compared to the uniform refinement.