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A symmetry relation of the integral operators in a layered medium proved by the reciprocal theory can be applied to improve the accuracy of the magnetic-field integral equation (MFIE). Based on the symmetric layered medium Green’s function, the normal vector can be transferred into the inner integral to keep the field integral as the inner integral of the elements in the impedance matrix. When discretized by the divergence-conforming function, this field-extracted scheme shows better performance than the classic expression in accuracy. Meanwhile, this form of expression can be applied in the combined-field integral equation (CFIE). Several numerical results are provided to validate the formulation of the symmetry relations from the layered medium Green’s function to the impedance matrices and to reveal its advantages in enhancing the accuracy of the field-extracted form of MFIE. [ABSTRACT FROM AUTHOR]

A quasi-mixed-potential layered medium Green’s function (QMP-LMGF) is proposed for non-Galerkin surface integral equation (SIE) formulations in the modeling of homogeneous dielectric objects in layered medium. The formulation is derived based on the pilot vector potential approach. In this method, the field-type LMGF in the $L$ -operator is decomposed into two parts, a “vector potential” term in a dyadic form, and a “scalar potential” term in a vector form, to represent the field components from current and charge sources, respectively. Since the proposed two potential terms (vector potential and scalar potential) do not satisfy the Lorenz gauge, we term them as quasi-mixed-potentials. The property of the two potentials is investigated to reveal that the proposed QMP-LMGF is compatible with the vector and scalar potentials in free space. Moreover, due to the continuity of the integration kernels across the interfaces, undesired line integrals are absent in the proposed QMP-LMGF when the objects are straddling different layers. Three popular non-Galerkin SIEs for dielectric objects in layered medium are studied, and the corresponding numerical results are demonstrated to validate the proposed method. [ABSTRACT FROM AUTHOR]

An efficient improved spectrum integral method (ISIM) is proposed to accelerate the scattering simulation of cuboid object by method of moment (MoM) in multiplanar layered medium (LM). The layered medium Green’s functions (LMGFs) are studied and decomposed into transmission and reflection terms, which hold the translational invariance and reverse translational invariance, respectively. By virtue of the (reverse) translational invariance of LMGF from the uniform square grids on the surface of the cuboid object, most of the coupling between the expanding basis functions and the testing basis functions can be represented by two kinds of submatrices, i.e., the Toeplitz matrix when transmission term is involved, and the conjugate Toeplitz matrix when reflection term is involved. Moreover, the submatrix coupling the expanding/testing basis functions defined on the edges with those defined on the parallel surfaces/edges is also extended to the (conjugate) Toeplitz matrixes. This will significantly alleviate the heavy computation and memory burden from the conventional SIM. With the improved operations on the basis functions associated with the edges of the cuboid object, the proposed ISIM in LM can reach the computational complexity as low as ${O}$ (${N} ^{1.5}$ log(N)) in the matrix vector production, while the computational complexity of matrix filling and the memory requirement are both ${O}$ (${N}^{1.5}$). Moreover, compared with conventional SIM, both theoretical analysis and numerical results demonstrate that the memory requirement and matrix filling time are dramatically decreased. [ABSTRACT FROM AUTHOR]

For perfectly electric conducting (PEC) objects, one difference between the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE) is related to the solid angle, which only exists in the latter. In this communication, the correct computation of solid-angle contribution in MFIE is first summarized and clarified. Through testing strictly inside triangles (TSIT) and testing on edges (TOE) with or without the correct limit value (CLV) for the solid-angle integral, six versions of MFIE are then implemented by utilizing Rao–Wilton–Glisson (RWG) functions for expansion and utilizing RWG or rotated Buffa–Christiansen (BC) functions for testing. Based on the simulations of typical sharp-edged targets and a sphere by the EFIE and six MFIEs, it is found that using CLVs for the solid-angle integral will improve the simulation accuracy substantially in comparison to that with incorrect limit values (ILVs). Moreover, if the singularities are properly handled, the MFIE implemented by TSIT can achieve the same accuracy with the MFIE implemented by TOE with CLVs. [ABSTRACT FROM PUBLISHER]