Solution of volume‐surface integral equations using higher‐order hierarchical Legendre basis functions

Abstract

[1] The problem of electromagnetic scattering by composite metallic and dielectric objects is solved using the coupled volume-surface integral equation (VSIE). The method of moments (MoM) based on higher-order hierarchical Legendre basis functions and higher-order curvilinear geometrical elements is applied to transform the VSIE into a system of linear equations. The higher-order MoM provides significant reduction in the number of unknowns in comparison with standard MoM formulations using low-order basis functions, such as RWG functions. Owing to the orthogonal nature of the higherorder Legendre basis functions, the continuity condition at the interface between metal and dielectric can be satisfied explicitly, which further reduces the number of unknowns as well as improves the accuracy of the solution. Numerical results for a metallic sphere with dielectric coating show excellent agreement with the analytical Mie series solution. Scattering by more complex metal-dielectric objects is also considered to compare the presented technique with other numerical methods.

The Application of Improved Spherical Harmonics Expansion-Based Multilevel Fast Multipole Algorithm in the Solution of Volume-Surface Integral Equation

“…Besides, for L = 5, both P = 2 and 3 yield accurate results, while P = 1 leads to an obviously unacceptable deviation. The case L = 3 also shows an unacceptable deviation but is closer to the L = 5 results than P = 1, which phenomenon is the same as stated in [2].…”

“…In the computational electromagnetics, the method of moments (MoM) solution of volume-surface integral equation (VSIE) is an attractive approach, since it can be generally applied to the simulation of the arbitrary composite conductor-inhomogeneous dielectric objects [1][2][3][4][5]. As one of the most powerful fast solvers, the multilevel fast multipole algorithm (MLFMA) can make MoM be applied to the analysis of objects with large electrical size [4][5][6][7][8].…”

Double-Higher-Order Large-Domain Volume/Surface Integral Equation Method for Analysis of Composite Wire-Plate-Dielectric Antennas and Scatterers

“…> AP1204-0439.R2< According to this approach, a structure is approximated by a number of as large as possible geometrical elements, and the approximation of current (or field) components within individual elements is in the form of a single (three-fold) functional series of sufficiently high order. Only relatively recently the computational electromagnetics (CEM) community has started to extensively investigate and employ higher order surface and volume elements and higher order basis functions in the frame of MoM, including the SIE formulation [16]- [19], VIE approach [20]- [29], and VSIE hybrid [30]- [34], as well as the finite element method (FEM) [35]- [38].…”

“…On the other hand, when compared with the alternative higher order VIE and VSIE scattering techniques [24]- [29], [33], and [34], the proposed technique is a wire-platedielectric antenna/scattering code. In addition, the present work demonstrates a dramatic improvement of results when using geometrical modeling of the 4th order instead of the 2nd order geometrical modeling, as well as the first singleelement, literally entire-domain, models of 3-D scatterers of general shapes (note that such an entire-domain solution to open-region problems is unique not only looking at existing VIE methods but at all available CEM methods overall).…”

Adaptive Integral Method for Higher Order Method of Moments

“…The AIM technique presented in the previous section has been implemented for the volume and volume-surface integral equations solved with the higher order MoM as described in [11] and [18], respectively. In all simulations, the generalized minimal residual (GMRES) iterative algorithm with restarts after 30 iterations has been employed.…”