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.

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 A Hybrid 3DMLUV-FIA Method for Scattering from a 3D Dielectric Object above a 2D Dielectric Rough Surface

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Wu Xuezhi ◽  
Wenping Yu
Keyword(s):  
Rough Surface ◽  
Method Of Moments ◽  
Electromagnetic Scattering ◽  
Three Dimensional ◽  
Memory Consumption ◽  
Scattering Problems ◽  
The Matrix ◽  
Speed Up ◽  
Stability And Accuracy ◽  
Time Overhead

The electromagnetic scattering from the composite model of a three-dimensional (3D) dielectric object located above a two-dimensional (2D) dielectric rough surface is analyzed in this work. Poggio, Miller, Chang, Harrington, Wu, and Tsai (PMCHWT) integral equations are discretized by the method of moments (MoM) into a matrix which is solved by Biconjugate Gradients Stabilized (BICGSTAB) method. Method of 3DMLUV was used for PEC object located above rough surface. Comparing to the case when object and rough surface are both PEC, the memory requirement and computational complexity for dielectric models are increased due to doubled unknown number. Moreover, compared to dielectric object in free space, the coupling between dielectric object and dielectric rough surface will result in complicated numerical simulation. To solve this problem, the updated rank based 3D Multilevel UV (3DMLUV) method is employed to reduce memory consumption and CPU time overhead. The 3DMLUV has been successfully applied in the scattering of PEC targets; however, when the object or rough surface becomes dielectric, the coupling between dielectric object and dielectric rough surface will lead to slow constriction. Therefore, the Fast Iterative Approach (FIA) is applied to further speed up the constricted speed of the matrix required in 3DMLUV. The efficiency, stability, and accuracy of the proposed method are demonstrated in a variety of scattering problems.

Advanced three-dimensional electromagnetic modeling using a nested integral equation approach

2021 ◽  
Author(s):  
Chaojian Chen ◽  
Mikhail Kruglyakov ◽  
Alexey Kuvshinov
Keyword(s):  
Integral Equation ◽  
Three Dimensional ◽  
Region Of Interest ◽  
Electromagnetic Modeling ◽  
Multi Scale ◽  
Scale Modeling ◽  
Uniform Grids ◽  
The Matrix ◽  
Integral Equation Approach ◽  
Matrix Vector

Summary Most of the existing three-dimensional (3-D) electromagnetic (EM) modeling solvers based on the integral equation (IE) method exploit fast Fourier transform (FFT) to accelerate the matrix-vector multiplications. This in turn requires a laterally-uniform discretization of the modeling domain. However, there is often a need for multi-scale modeling and inversion, for instance, to properly account for the effects of non-uniform distant structures, and at the same time, to accurately model the effects from local anomalies. In such scenarios, the usage of laterally-uniform grids leads to excessive computational loads, both in terms of memory and time. To alleviate this problem, we developed an efficient 3-D EM modeling tool based on a multi-nested IE approach. Within this approach, the IE modeling is first performed at a large domain and on a (laterally-uniform) coarse grid, and then the results are refined in the region of interest by performing modeling at a smaller domain and on a (laterally-uniform) denser grid. At the latter stage, the modeling results obtained at the previous stage are exploited. The lateral uniformity of the grids at each stage allows us to keep using the FFT for the matrix-vector multiplications. An important novelty of the paper is a development of a “rim domain” concept which further improves the performance of the multi-nested IE approach. We verify the developed tool on both idealized and realistic 3-D conductivity models, and demonstrate its efficiency and accuracy.

scholarly journals Combination of MLFMA and ACA to Accelerate Computation of Scattering from Underground Targets

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Zhiwei Liu ◽  
Dan Tang ◽  
Zhanyang Zhang ◽  
Yueyuan Zhang ◽  
Xiaoli Wang ◽  
...  
Keyword(s):  
Integral Equation ◽  
Nondestructive Evaluation ◽  
Method Of Moments ◽  
Impedance Matrix ◽  
Computation Complexity ◽  
Surface Integral ◽  
Efficient Simulation ◽  
Urban Construction ◽  
Multilevel Fast Multipole Algorithm ◽  
Fast Multipole Algorithm

Electromagnetic nondestructive evaluation of underground targets is of great significance for the safety of urban construction. Based on the accurate and efficient simulation of scattering, we can detect the underground targets successfully. As one of the most popular numerical methods in electromagnetics, surface integral equations solved by method of moments (MoM) are used to simulate the scattering from underground targets in this paper. The integral equation is discretized by RWG basis and Galerkin testing. Multilevel fast multipole algorithm (MLFMA) is used to decrease the computation complexity and memory cost. However, the octree used in MLFMA is not applied for rough surfaces and targets together; both the surface and target need to construct octree separately. Since the combination of MLFMA and ACA can build a more efficient method to compute scattering from underground targets, adaptive cross approximation (ACA) is used to compress the impedance matrix instead of MLFMA for the coupling action between the rough surface and target. That is to say that, when calculating the scattering of two targets, target self-interaction is suitable for MLFMA calculation and the coupling between targets is approximated by ACA. Numerical results demonstrate the accuracy and efficiency of our proposed method.

scholarly journals Parallel Integral Equation-Based Nonoverlapping DDM for Solving Challenging Electromagnetic Scattering Problems of Two Thousand Wavelengths

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Qin Su ◽  
Yingyu Liu ◽  
Xunwang Zhao ◽  
Zongjing Gu ◽  
Chang Zhai ◽  
...  
Keyword(s):  
Integral Equation ◽  
Electromagnetic Scattering ◽  
Domain Decomposition Method ◽  
Near Field ◽  
Limited Resources ◽  
Accurate Analysis ◽  
Scattering Problems ◽  
Fast Multipole Algorithm ◽  
Matrix Vector ◽  
Field Integral

In this paper, a parallel nonoverlapping and nonconformal domain decomposition method (DDM) is proposed for fast and accurate analysis of electrically large objects in the condition of limited resources. The formulation of nonoverlapping DDM for PEC bodies is derived from combined-field integral equation (CFIE), and an explicit boundary condition is applied to ensure the continuity of electric currents across the boundary. A parallel multilevel fast multipole algorithm (MLFMA) is extended to accelerate matrix-vector multiplications of subdomains as well as the coupling between them, and the coupling between different subdomains is computed in the manner of near field to avoid the storage of the mutual impedance. An improved adaptive direction partitioning scheme is applied to the oct-tree of MLFMA to achieve high parallel efficiency. Numerical examples demonstrate that the proposed method is able to simulate realistic problems with a maximum dimension greater than 2000 wavelengths.

scholarly journals A fast three-dimensional deterministic ray tracing coverage simulator for a 24 GHz anti-collision radar

2013 ◽  
Vol 11 ◽  
pp. 55-60 ◽  
Author(s):  
H. Azodi ◽  
U. Siart ◽  
T. F. Eibert
Keyword(s):  
Integral Equation ◽  
Ray Tracing ◽  
Collision Avoidance ◽  
Electromagnetic Fields ◽  
Method Of Moments ◽  
Three Dimensional ◽  
Frequency Independent ◽  
The Matrix ◽  
24 Ghz ◽  
Good Agreement

Abstract. A matrix-based approach for implementation of deterministic ray tracing is suggested and presented in this paper. The frequency-independent feature of the ray tracing in addition to the matrix-based implementation results in a reliable fast simulator for understanding the behavior of the electromagnetic fields in the vicinity of a collision avoidance radar. Results of this technique are in a good agreement with the results from method of moments integral equation solutions while the computations are about 100 times faster.

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.

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