scholarly journals SURFACE INTEGRAL EQUATION FORMULATION FOR THE ANALYSIS OF SINGLE AND MULTI-LAYER DIELECTRIC ANTENNAS

2020 ◽  
Author(s):  
John Stevenson
Keyword(s):  
Integral Equation ◽  
Electromagnetic Scattering ◽  
Fast Multipole Method ◽  
Three Dimensional ◽  
Dielectric Materials ◽  
Layered Composite ◽  
Surface Integral ◽  
Dielectric Resonator Antennas ◽  
Surface Integral Equation ◽  
Integral Equation Formulation

This article studies numerically the electromagnetic scattering properties of three dimensional (3D), arbitrary shaped dielectric resonator antennas which are composed of single and multi-layered (composite) dielectric materials. Using the equivalence principle and the integral equation techniques, we first derive a surface integral equation (SIE) formulation which produces well-conditioned matrix equation. We then develop an algorithm to speed up the matrix-vector multiplications by employing the well-known method of moments (MoM) and the multilevel fast multipole method (MLFMM) on personal computer (PC) clusters. To solve the obtained integral equations, we apply a Galerkin scheme and choose the basis and testing functions as Rao-Wilton-Glisson (RWG) defined on planar patches. Finally, we present some 3D numerical examples to demonstrate the validity and accuracy of the proposed approach.

scholarly journals Electromagnetic Scattering Analysis of SHDB Objects Using Surface Integral Equation Method

Photonics ◽  
2020 ◽  
Vol 7 (4) ◽  
pp. 134
Author(s):  
Beibei Kong ◽  
Pasi Ylä-Oijala ◽  
Ari Sihvola
Keyword(s):  
Boundary Condition ◽  
Integral Equation ◽  
Electromagnetic Scattering ◽  
Three Dimensional ◽  
Circular Disk ◽  
Integral Equation Method ◽  
Surface Integral ◽  
Three Dimensional Objects ◽  
Surface Integral Equation ◽  
Scalar Equations

A surface integral equation (SIE) method is applied in order to analyze electromagnetic scattering by bounded arbitrarily shaped three-dimensional objects with the SHDB boundary condition. SHDB is a generalization of SH (Soft-and-Hard) and DB boundary conditions (at the DB boundary, the normal components of the D and B flux densities vanish). The SHDB boundary condition is a general linear boundary condition that contains two scalar equations that involve both the tangential and normal components of the electromagnetic fields. The multiplication of these scalar equations with two orthogonal vectors transforms them into a vector form that can be combined with the tangential field integral equations. The resulting equations are discretized and converted to a matrix equation with standard method of moments (MoM). As an example of use of the method, we investigate scattering by an SHDB circular disk and demonstrate that the SHDB boundary allows for an efficient way to control the polarization of the wave that is reflected from the surface. We also discuss perspectives into different levels of materialization and realization of SHDB boundaries.

scholarly journals ANALYSIS OF COMPOSITE DIELECTRIC METAMATERIALS USING INTEGRAL EQUATION TECHNIQUES

2020 ◽  
Author(s):  
John Stevenson
Keyword(s):  
Integral Equation ◽  
Method Of Moments ◽  
Electromagnetic Scattering ◽  
Three Dimensional ◽  
Surface Integral ◽  
Integral Equation Formulation ◽  
The Matrix ◽  
Speed Up ◽  
Fast Multipole Algorithm ◽  
Matrix Vector

We study numerically the electromagnetic scattering properties of three dimensional (3D),arbitrary shaped composite dielectric metamaterials. Using integral equation techniques, we firstderive a surface integral equation formulation which produces well-conditioned matrix equation.To solve the obtained integral equations, we apply a Galerkin scheme and choose the basis andtesting functions as Rao-Wilton-Glisson defined on planar patches. We then develop an algorithmto speed up the matrix-vector multiplications by employing the well-known method of moments(MoM) and the multilevel fast multipole algorithm on personal computer (PC) clusters. Some 3Dnumerical examples are presented to demonstrate the validity and accuracy of the proposedapproach.

A Modified Hybrid Integral Equation to Electromagnetic Scattering from Composite PEC-Dielectric Objects Containing Closed-Open PEC Junctions

2021 ◽  
Vol 36 (6) ◽  
pp. 642-649
Author(s):  
Jinbo Liu ◽  
Hongyang Chen ◽  
Hui Zhang ◽  
Jin Yuan ◽  
Zengrui Li
Keyword(s):  
Integral Equation ◽  
Electromagnetic Scattering ◽  
Surface Integral ◽  
Electric Conductor ◽  
Electric Field Integral Equation ◽  
Surface Integral Equation ◽  
Hybrid Integral ◽  
Fast Solution ◽  
Dielectric Objects ◽  
Field Integral

To efficiently analyze the electromagnetic scattering from composite perfect electric conductor (PEC)-dielectric objects with coexisting closed-open PEC junctions, a modified hybrid integral equation (HIE) is established as the surface integral equation (SIE) part of the volume surface integral equation (VSIE), which employs the combined field integral equation (CFIE) and the electric field integral equation (EFIE) on the closed and open PEC surfaces, respectively. Different from the traditional HIE modeled for the objects whose closed and open PEC surfaces are strictly separate, the modified HIE can be applied to the objects containing closed-open junctions. A matrix equation is obtained by using the Galerkin’s method of moments (MoM), which is augmented with the spherical harmonics expansion-based multilevel fast multipole algorithm (SE-MLFMA), improved by the mixed-potential representation and the triangle/tetrahedron-based grouping scheme. Because in the improved SE-MLFMA, the memory usage for storing the radiation patterns of basis functions is independent of the SIE type in the VSIE, it is highly appropriate for the fast solution of the VSIE that contains the HIE. Various numerical experiments demonstrate that during the calculation of composite objects containing closed-open PEC junctions, the application of the modified HIE in the VSIE can give reliable results with fast convergence speed.

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