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Electromagnetic analysis for microstrip antenna and packaging structures is formulated by volume-surface integral equations (VSIEs). The conducting microstrip and ground are described with SIEs, while the dielectric substrate is governed by volume integral equations (VIEs), and they are coupled to each other to form VSIEs. Using VIEs instead of SIEs for dielectric substrate can improve the conditioning of system matrix related to the multiscale property of antenna and packaging structures. The VSIEs are usually solved by the method of moments (MoM) with well-designed basis functions defined over conforming meshes, resulting in much inconvenience of implementation. We propose a mixed approach to solve the VSIEs by combining the traditional MoM for the conducting part and a point-matching scheme for the dielectric part together. The approach uses cuboids to discretize the dielectric substrate and does not require conforming meshes between the conducting and dielectric parts. Also, the approach considers the thickness of metallic microstrip and ground, which is usually neglected. Typical numerical examples are presented to demonstrate the proposed approach, and its effectiveness has been verified.

A model-based inverse algorithm combined with the curl-conforming volume integral equation method is presented for inversion of anisotropic material permittvities from scattered fields. The forward algorithm uses the curl-conforming volume integral equation method. The inversion algorithm is based on the Gauss-Newton method. Numerical examples show the effectiveness of the inversion algorithm and demonstrate the sensitivities of measurements to the anisotropic objects.

Volume integral equations (VIEs) are indispensable to formulate inhomogeneous or anisotropic electromagnetic (EM) problems and cuboid meshes are preferred to discretize volume domains in some applications. In solving the VIEs, accurate evaluation for singular integrals is very essential but there is no direct method to evaluate hypersingular integrals over a cuboid domain so far. In this work, we propose some closed-form formulas for calculating those hypersingular volume integrals and they are simpler and more efficient to implement. A numerical example is presented to demonstrate the formulas and their effectiveness has been verified.

Electromagnetic (EM) scattering by bi-isotropic objects is formulated through volume integral equations (VIEs). The VIEs are usually solved by the method of moments (MoM) in which unknown flux densities are expanded with the Schaubert-Wilton-Glisson (SWG) or other divergence-conforming basis functions, but the approach may not be convenient in implementation because material parameters are involved in integrands. We propose a point-matching scheme to solve the VIEs in which current densities are selected as unknown functions to be solved and integral kernels are free of material parameters, resulting in a facilitation of implementation for bi-isotropic media. A typical numerical example is presented to demonstrate the scheme and its robustness has been verified.