A FESI Domain Decomposition Method for EM Scattering by Multiscale Objects With Multiple Interior/Exterior Spherical Couplings

This article presents a novel function space framework for coupled finite element (FE)-spectral integral (FESI) analysis of electromagnetic (EM) scattering problems involving multiscale objects at different orientations and locations with an arbitrary number of interior/exterior spherical coupling interfaces. The hybrid methodology combines the complementary strengths of both techniques: FE resolves internal fields in intricate inhomogeneous structures through localized discretization, while vector spherical harmonics (VSHs) rigorously handles boundary integral equations for coupling the external field incident and radiation via spectral operators. A topology-aware matrix preallocation technique accelerates parallel discretization and assembly of the function space, leveraging inherent sparsity facilitating efficient preconditioner construction. Spectral convergence is achieved in iterative solutions for multidomain configurations. Computational complexity can be reduced through iterative substructuring for domains with repetitive geometries, while maintaining extensibility to distributed parallel computing architectures. Numerical validation via Friis transmission formula, EM scattering of unmanned aerial vehicle (UAV) swarms, and radiation patterns of radome-enclosed Cassegrain antenna arrays confirms the accuracy and computational efficiency of FESI.