On the Use of a Localized Huygens' Surface Scheme for the Adaptive H-Refinement of Multiscale Problems

This work proposes a domain decomposition method (DDM) based on Huygens' equivalence principle to efficiently perform an adaptive h-refinement technique for the electromagnetic analysis of multiscale structures via surface integral equations (SIEs). The procedure starts with the discretization of the structure under analysis via an initial coarse mesh, divided into domains. Then, each domain is treated independently, and the coupling to the rest of the object is obtained through the electric and magnetic current densities on the equivalent Huygens' surfaces (EHSs), surrounding each domain. From the initial solution, the error is estimated on the whole structure, and an adaptive h-refinement is applied accordingly. Both the error estimation and the adaptive h-refined solution are obtained through the defined EHSs, keeping the problem local. The adaptive h-refinement is obtained by a nonconformal submeshing, where multibranch Rao-Wilton-Glisson (MB-RWG) basis functions are defined. Numerical experiments of multiscale perfect-electric-conductor (PEC) structures in air, analyzed via the combined field integral equation, show the performance of the proposed approach.