Computation of Tensor Green’s Functions in Uniaxial Planar-Stratified Media With a Rescaled Equivalent Boundary Approach

Xing, Guang Zhong; Zhang, Xiaochong; Teixeira, F.L.

doi:10.1109/tap.2018.2803210

Cited by 8 publications

(9 citation statements)

References 30 publications

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“…This is more complicated using MoM directly solving electric integral equation (EFIE) for the unknown electric currents in half-space than in free-space, because the planar stratified-medium Green's functions is dyadic form, and comprises Sommerfeld-type integrals, which are extremely laborious to evaluate by using discrete complex image method (DCIM). [14][15][16][17][18][19][20] Fortunately, Michalski and ZHENG derive this complicated integral in Michalski and Mosig, Michalski, and Michalski and Zheng 17,20,21 in detail, respectively. Moreover, Michalski and Zheng describe several possible choices for dyadic Green's FIGURE 1 Geometry for derivation of dyadic Green's functions of general planner multilayered environment functionG Amn r; r ′ À Á .…”

Section: Methods Of Moments In Half-spacementioning

confidence: 99%

“…The half‐space environment belongs to the planar stratified‐medium, as shown in Figure . This is more complicated using MoM directly solving electric integral equation (EFIE) for the unknown electric currents in half‐space than in free‐space, because the planar stratified‐medium Green's functions is dyadic form, and comprises Sommerfeld‐type integrals, which are extremely laborious to evaluate by using discrete complex image method (DCIM) . Fortunately, Michalski and ZHENG derive this complicated integral in Michalski and Mosig, Michalski, and Michalski and Zheng in detail, respectively.…”

Section: Formulationsmentioning

confidence: 99%

“…Setting k = 1,2, …, at ( k + 1)th step, the unknown current coefficients can be expressed as

I_{i}^{(k + 1)} = - A_{ii}^{- 1} \sum_{j < i} C_{ij} I_{j}^{(k + 1)} - A_{ii}^{- 1} \sum_{j > i} C_{ij} I_{j}^{(k)} + A_{ii}^{- 1} V_{i} .

Specially, the product ∆ V i ( k ) of C ij and I j ( k ) ( j > i ) or ∆ V i ( k + 1) of C ij and I j ( k + 1) ( j < i ) can be obtained using near field produced by the current

Δ {boldV}_{i}^{(k)} bold= C_{ij} {boldI}_{j}^{(k)} = \int_{S^{i}} f_{n} ((), {boldr}^{'}) {boldE}_{i}^{(k)} ((), J) ds, ((), i \neq j)

where S i is the exterior boundary of subdomain Ω i , and E i ( k ) denotes the nearfield of subdomain Ω i produced by the rest subdomains at k th step. Hence, the memory requirement and CPU time are reduced greatly . And the relative residual error at k th iteration is used to express the convergence behavior of the Gauss‐Seidel iterative procedure, which is defined as

δ_{i} = \frac{(‖‖, {boldI}_{i}^{k + 1} - {boldI}_{i}^{k})}{‖{boldI}_{i}^{k + 1}‖} .

The iteration procedure is terminated when max( δ 1 , δ 2 , …, δ n ) < δ is satisfied.…”

Section: Formulationsmentioning

confidence: 99%

“…This novel IE‐NDDM technique accelerates the calculation of the EM characteristics of PEC targets in a remarkable way but keeping the same level of accuracy than pure techniques such as MoM (see Section for further details about computational time and accuracy comparisons). Additionally, the proposed IE‐NDDM treats the scattering problem in half‐space similar to free‐space by introducing the dyadic Green's function

{\overset{true¯}{boldG}}_{Amn} ((), boldr, r^{'})

, where the influence of the half‐space background is taken into account . Compared with overlapped DDM, the IE‐NDDM proposed in this paper only adds artificial touching faces between adjacent subdomains to make each of them closed.…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, the proposed IE-NDDM treats the scattering problem in half-space similar to free-space by introducing the dyadic Green's functionG Amn r; r ′ À Á , where the influence of the half-space background is taken into account. [15][16][17][18][19] Compared with overlapped DDM, 7-10 the IE-NDDM proposed in this paper only adds artificial touching faces between adjacent subdomains to make each of them closed. And an explicit transmission condition is adopted to enforce the electric current continuity across adjacent subdomains.…”

Section: Introductionmentioning

confidence: 99%

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Integral equation‐based nonoverlapping domain decomposition method for electromagnetic scattering analysis of PEC targets in half‐space environment

Zhao

Lin

2019

Int J Numerical Modelling

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An integral equation‐based nonoverlapping domain decomposition method (IE‐NDDM) is proposed for efficient and accurate scattering analysis of electrically large PEC targets in a half‐space environment. Taking the condition that there are null fields as well as current inside PEC objects in the original problem, a novel explicit transmission condition is proposed to ensure continuity of electric currents between adjacent subdomains. Moreover, to deal with this situation that targets located in half‐space environment, the stratified‐medium dyadic Green's function is adopted. Numerical examples are provided to demonstrate the correctness and the performance of the proposed method. In detail, an analysis about electromagnetic scattering respect to the altitude of the target away from half‐space interface, the incident direction of plane wave, and the material parameters of the lower half‐space is presented; furthermore, the convergence behavior of the proposed method is studied.

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Section: Methods Of Moments In Half-spacementioning

confidence: 99%

Section: Formulationsmentioning

confidence: 99%

“…Setting k = 1,2, …, at ( k + 1)th step, the unknown current coefficients can be expressed as

I_{i}^{(k + 1)} = - A_{ii}^{- 1} \sum_{j < i} C_{ij} I_{j}^{(k + 1)} - A_{ii}^{- 1} \sum_{j > i} C_{ij} I_{j}^{(k)} + A_{ii}^{- 1} V_{i} .

Specially, the product ∆ V i ( k ) of C ij and I j ( k ) ( j > i ) or ∆ V i ( k + 1) of C ij and I j ( k + 1) ( j < i ) can be obtained using near field produced by the current

Δ {boldV}_{i}^{(k)} bold= C_{ij} {boldI}_{j}^{(k)} = \int_{S^{i}} f_{n} ((), {boldr}^{'}) {boldE}_{i}^{(k)} ((), J) ds, ((), i \neq j)

δ_{i} = \frac{(‖‖, {boldI}_{i}^{k + 1} - {boldI}_{i}^{k})}{‖{boldI}_{i}^{k + 1}‖} .

The iteration procedure is terminated when max( δ 1 , δ 2 , …, δ n ) < δ is satisfied.…”

Section: Formulationsmentioning

confidence: 99%

{\overset{true¯}{boldG}}_{Amn} ((), boldr, r^{'})

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Integral equation‐based nonoverlapping domain decomposition method for electromagnetic scattering analysis of PEC targets in half‐space environment

Zhao

Lin

2019

Int J Numerical Modelling

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Numerical Simulation and Analysis of Multicomponent Induction Logging Response in Anisotropic Formation

Sun

et al. 2020

IEEE Access

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In this article, the response characteristics of multicomponent induction logging (MCIL) tool in anisotropic formation are analyzed. To solve the 1-D MCIL problems, we use a planar layered anisotropic medium (PLAM) Green's function (PLAMGF) method which is derived from the layered-medium Green's function (LMGF) and combined with MCIL excitation source and anisotropic formation environment, and then use it to investigate the equivalence of the MCIL tool responses in two models, i.e. the microscopic thin interbed formation and macroscopic anisotropic formation, and also analyze the effects of shoulder bed and formation dip on MCIL tools. In addition, in order to solve the complex 3-D problems, such as the effects of borehole, tool eccentricity and invasion on the tool response, we use the finite element method (FEM) based on a proposed new meshing scheme to simulate and analyze. This new meshing scheme includes two aspects: the use of cylindrical hexahedron element and the flexible meshing strategy combined with domain decomposition. Finally, some key detection performances of coaxial coils and coplanar coils of MCIL tool are studied. Numerical experiments are conducted to prove the effectiveness of our proposed method and provide the detailed results of the aforementioned aspects.INDEX TERMS Multicomponent induction logging (MCIL), Green's function (GF), electric anisotropy, finite element method (FEM).

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Spectral Dyadic Green’s Function for Multilayer Periodic Bi-Anisotropic Media

Rafaei-Booket

Bozorgi

2022

IEEE Access

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A computational technique for evaluating the spectral dyadic Green's function utilized in the analysis of multilayer structures composed of periodic bi-anisotropic layers is presented. The Green's function is achieved with the help of a fully vectorial rigorous matrix formulation based on a generalized transmission line (TL) formulation of Maxwell's equations. This matrix formulation simplifies the mathematics involved in the modeling of the coupled diffraction orders within a periodic bi-anisotropic layer. To examine the soundness of this modeling, the extracted Green's function is used in an integral equation for the analysis of metallic gratings on homogeneous/inhomogeneous anisotropic and chiral materials. The resulting integral equation is then solved by the Method of Moments (MoM) formulated in terms of sub-domain basis and Galerkin's test functions. As verification, several examples are analyzed and the results obtained by this method are compared with those available in the literature or obtained by EMsolvers. The efficiency assessment of this method is carried out by considering its convergence rate and cost-time in terms of truncation orders. It is revealed not only the metallic grating with inhomogeneous periodic bi-anisotropic layers can be analyzed by this method but also analysis time, memory, and CPU occupancies are decreased in comparison with commercial EM-solvers.INDEX TERMS Spectral dyadic Green's function, Periodic bi-anisotropic media, Transmission Line (TL) modeling, Method of Moments (MoM).

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Computation of Tensor Green’s Functions in Uniaxial Planar-Stratified Media With a Rescaled Equivalent Boundary Approach

Cited by 8 publications

References 30 publications

Integral equation‐based nonoverlapping domain decomposition method for electromagnetic scattering analysis of PEC targets in half‐space environment

Integral equation‐based nonoverlapping domain decomposition method for electromagnetic scattering analysis of PEC targets in half‐space environment

Numerical Simulation and Analysis of Multicomponent Induction Logging Response in Anisotropic Formation

Spectral Dyadic Green’s Function for Multilayer Periodic Bi-Anisotropic Media

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