Metasurfaces are thin metamaterial layers characterized by unusual dispersion properties of surface/guided wave and/or reflection properties of otherwise incident plane waves. At the scales intervening in their design, metasurfaces can be described through a surface impedance boundary condition. The impedance, possibly tensorial, is often “modulated,” i.e., it can vary from place to place on the surface (by design). We investigate on different integral equation formulations of the problem, with special attention to the stability properties of the resulting system matrix.

We propose a method to significantly improve the spectral properties of the EFIE MoM matrix for broad-band analysis of structures with fine details, non-uniform meshes, and large overall sizes. A multilevel approach allows to overlay fine meshes and quasi-Nyquist sampled meshes; the fine-mesh conditioning is solved via hierarchical basis functions, and the quasi-Nyquist sampled part is treated by an algebraic incomplete LU preconditioner. Numerical results show the effectiveness of the approach for several realistic structures with overall sizes of ten/twenty wavelengths and levels of detail from very moderate to extending over the whole structure.

We present a domain decomposition (DD) framework for the analysis of impenetrable structures; it allows for the electric field integral equation (EFIE) and combined field integral equation (CFIE), and for open, closed, and open-closed structures. The DD results in an effective preconditioner for large and complex problems exploiting iterative solution and fast factorizations. The DD employs specialized transmission conditions among the domains, and the use of discontinuous Galerkin (DG) allows conformal as well as nonconformal discretizations of domain boundaries; the nonconformal nature of the decomposition gives considerable flexibility in the meshing. The strategy is highly parallelizable, as all the operations involving the subdomains can be performed in parallel. The proposed scheme is implementation independent and can be easily merged with existing electromagnetic codes.

We introduce a method to compress the impedance matrix of the method of moments (MoM) for the modeling of high-fidelity multiscale structures at low- to moderate-frequencies. We start from a method recently proposed to compress static (scalar) problems, proved to have O(N) computational complexity. We represent far coupling between groups through equivalent source distributions on properly defined, automatically generated equivalence surfaces. The equivalent sources are obtained via an inverse-source process that enforces equivalence of radiated fields on testing surfaces within a prescribed accuracy, and are intrinsically multiscale. This results in an O(N) complexity scaling of matrix-vector products, but reduces multiplicative constants (i.e., reduces time and memory requirements) for all structures. It affords an improved representation of couplings in multiscale structures, resulting in a fast convergence of iterative solvers. Our approach is Green's function independent and easy to be implemented in existing MoM codes; the present version is based on the electric field integral equation (EFIE). Numerical results prove the effectiveness of the proposed algorithm for complex multiscale structures.

In this letter, we present the analysis of large multiscale wire-surface structures through the method of moments (MoM) discretization of the electric field integral equation (EFIE). The MoM system is solved via the Green's function interpolation with fast Fourier transform (GIFFT) fast solver, extended here to geometries with wires and wires connected to surfaces. The implemented solver is entirely integrated with a hierarchical hybrid preconditioner, to allow an efficient analysis, in terms of computational time and memory requirements, of realistic and topologically complex geometries.

We propose a wideband fast kernel-independent modeling of large multiscale structures; we employ a nested equivalent source approximation (NESA) to compress the dense system matrix. The NESA was introduced by these authors for low and moderate frequency problems (smaller than a few wavelengths); here, we introduce a high-frequency NESA algorithm, and propose a hybrid version with extreme wideband properties. The equivalent sources of the wideband NESA (WNESA) are obtained by an inverse-source process, enforcing equivalence of radiated fields on suitably defined testing surfaces. In the low-frequency region, the NESA is used unmodified, with a complexity of O(N). In the high-frequency region, in order to obtain a fixed rank matrix compression, we hierarchically divide the far coupling space into pyramids with angles related to the peer coupling group size, and the NESA testing surfaces are defined as the boundaries of the pyramids. This results in a directional nested low-rank (fixed rank) approximation with O(N log N) computational complexity that is kernel independent; overall, the approach yields wideband fast solver for the modeling of large structures that inherits the efficiency and accuracy of low-frequency NESA for multiscale problems. Numerical results and discussions demonstrate the validity of the proposed work.