Li Zhang

Interactions of transient electromagnetic (EM) waves with homogeneous penetrable bodies are governed by the temporal-domain Poggio-Miller-Chang-Harrington-Wu-Tsai equations (TD-PMCHWTEs) or Müller equations (TD-MEs) and they can be unified as temporal-domain surface integral equations (TD-SIEs). The TD-SIEs can be solved by using the traditional approach where the spatial domain is discretized by the method of moments (MoM) while the temporal domain is discretized by the scheme of march on in time (MOT). However, the MoM requires an expensive conformal-mesh discretization for geometries and the MOT scheme gives rise to a later-period instability issue. This paper proposes a mixed approach to resolve the TD-SIEs where the spatial domain is discretized by the Nyström scheme while the temporal domain is discretized by a Galerkin's scheme where the Laguerre function is used as a basis function and testing function. In this way, the discretization of TD-SIEs in spatial domain can be greatly simplified and an unconditional stability can be realized in temporal domain. The proposed approach is validated by numerical experiments and its expected performance has been achieved.

Some objects like mineral substances may be both dielectric and magnetic and their high-resolution inner imaging is very desirable when detecting and analyzing their ingredients. An integral equation method is developed for reconstructing or imaging such objects by using microwave illumination. Since the objects are both dielectric and magnetic, full volume integral equations (VIEs) are needed to describe the problem. The objects can be reconstructed by alternatively solving the forward scattering VIEs (FSVIE) and the inverse scattering VIEs (ISVIEs) under the Born iterative method (BIM) or distorted BIM (DBIM). The Nyström method is used to solve the FSVIEs while a Gauss-Newton minimization method (GNMM) with a multiplicative regularization scheme (MRS) is employed to solve the ISVIE. The Nyström method is more suitable for solving the FSVIEs of inverse problems because it is a point-matching method. To accelerate the solution, the multilevel fast multipole algorithm (MLFMA) is incorporated with the Nyström method which is new for solving inverse problems. Also, using the MRS-based GNMM to solve the ISVIEs can facilitate the selection of regularization parameter and reduce the requirements on measured data. Numerical examples are provided to demonstrate the approach and good results have been achieved.

Real conductors of interconnect structures are lossy and their skin depth becomes large at low frequencies. The traditional one-region formation with the approximation of perfectly electric conductors (PECs) or surface impedances may not be valid anymore and two-region integral equation formations are needed in the integral equation approach. Also, the electric field integral equation (EFIE) tends to break down at low frequencies and augmented electric field integral equation (AEFIE) has been proposed to remedy the problem. In this work, we treat lossy conductors as penetrable objects and propose two-region augmented hybrid field integral equations (AHFIEs) for low-frequency analysis. The HFIEs consist of the EFIE of describing the exterior of a conductor and the magnetic field integral equation (MFIE) of describing its interior. Since the magnetic current density appears in the L operator in the HFIEs, we select the magnetic charge density as a new unknown function to be solved and introduce the continuity equation of magnetic current density as an extra equation. By incorporating the volume integral equations (VIEs) of describing the substrate with arbitrary penetrable media in the interconnect structures, the two-region augmented volume-surface integral equations (AVSIEs) are formulated for entire structures. The AVSIEs are solved by the method of moments (MoM) where the Rao-Wilton-Glisson (RWG) and Schaubert-Wilton-Glisson (SWG) basis functions are used to represent the surface current densities of AHFIEs and volume current densities of VIEs, respectively, while a pulse basis function is employed to represent the charge densities of AHFIEs. Numerical examples are presented to illustrate the approach and good results have been obtained.

Electromagnetic problems with both conducting and anisotropic media are formulated by volume-surface integral equations (VSIEs). The conducting medium is described by a surface integral equation while the anisotropic medium is governed by volume integral equations (VIEs) and they are coupled together via produced fields. The VSIEs are usually solved by the method of moments (MoM) in which the electric current density on the conductor surface is expanded by the Rao-Wilton-Glisson basis function while the volumetric flux densities inside the anisotropic medium are represented by the Schaubert-Wilton-Glisson basis function. In this work, we use a point-matching scheme to discretize the VIEs of dielectric part and couple it with the MoM for the conducting part. We also incorporate the hybrid scheme with the multilevel fast multipole algorithm to accelerate the solving process for electrically large problems. A numerical example is provided to illustrate the approach and good results have been obtained.

This paper mainly addresses the accurate solution of electromagnetic scattering by 3D conducting objects based on Nyström method. The surface integral equation model of the conductor is constructed by surface triangles. The singularity of the near-field points is corrected by replacing the original source points with new points in the triangles and combining the Duffy’s transform and Gauss-Legendre quadrature rule. The accuracy of numerical solutions is demonstrated with an example.