Singularity Problem With the One-sheet Huygens Subgridding Method

Altameemi, Hayder Wathik; Bérenger, Jean-Pierre; Costen, Fumie

doi:10.1109/temc.2016.2624511

Cited by 5 publications

(4 citation statements)

References 8 publications

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“…The B-scan images by the two algorithms are illustrated in Figs. 6 (2) and (3), respectively. As shown in Fig.…”

Section: Gpr B-scan Image Of Buried Cylindersmentioning

confidence: 99%

“…The main difficulty of subgridding technique is the reduced accuracy and late-time instability due to the temporal and spatial interpolations, especially when a grid contrast ratio is large. The large grid contrast ratio with high accuracy was achieved by the Huygens subgridding algorithm [5], [6], but it usually has fairly higher late-time instability. The FDTD subgridding algorithm with separated temporal and spatial subgridding interfaces [7] has higher late-time stability by using two subgridding interfaces for temporal and spatial interpolations separately, but has lower accuracy due to the electric and magnetic field are discontinuous at temporal subgridding interface.…”

Section: Introductionmentioning

confidence: 99%

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A Novel Transformation Optics-Based FDTD Algorithm for Fast Electromagnetic Analysis of Small Structures in a Large Scope

et al. 2019

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In this paper, we present a novel Transformation Optics based Finite-difference time-domain (TO-FDTD) algorithm with Square Transformed Region, which is suitable for fast electromagnetic analysis of small structures in a large computational domain. A small structure can be solved with coarse grids in a transformed region, since it is enlarged by transformation optics. No fine grid is applied for the small structure so that computational efficiency can be improved greatly. In addition, the TO-FDTD algorithm can also avoid time-space field interpolations and the late-time instability of the subgridding algorithm. To eliminate the staircasing errors introduced by curved boundaries of its transformed region, we propose the square transformed region instead of the circular one. We parameterize the square boundary in polar coordinates so that it is easy to be implemented. Through coordinate transformation, new anisotropic permittivity and permeability can be obtained in the transformed region. Then we develop a stable anisotropic FDTD algorithm to solve the transformed Maxwell's Equations. Numerical results on diffraction and scattering of small structures show that our proposed TO-FDTD algorithm has high computational efficiency and accuracy.INDEX TERMS Finite-difference time-domain (FDTD), staircasing errors, transformation optics.

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“…The B-scan images by the two algorithms are illustrated in Figs. 6 (2) and (3), respectively. As shown in Fig.…”

Section: Gpr B-scan Image Of Buried Cylindersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Novel Transformation Optics-Based FDTD Algorithm for Fast Electromagnetic Analysis of Small Structures in a Large Scope

et al. 2019

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“…Because the uniformly fine mesh of the FDM will result in a very large memory cost and the extension of the iterations. To solve this issue, some subgridding algorithms, such as a variable step size method (VSSM) [13], a spatial subgridding algorithm with separated temporal and spatial interfaces [14], a hybrid implicit-explicit FDTD method (HIE-FDTD) [15], and a Huygens subgridding FDTD method [16] were proposed and successfully applied in solving Maxwell equations. Since at least two sizes of grids are applied to the subgridding algorithm and the time steps of the domains with different grid sizes can be different, the simulations of the coarse grid and the fine grid can be carried out separately.…”

Section: Introductionmentioning

confidence: 99%

A Difference Subgridding Method for Solving Multiscale Electro-Thermal Problems

2022

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Because of less memory costs and time consumption, a finite difference subgrid technique can effectively deal with multiscale problems in electromagnetic fields. When used in Maxwell equation, symmetric elements of the matrix are required; otherwise, the algorithm will be unstable. Usually, the electro-thermal problem also contains multiscale structures. However, the coefficient matrix of the heat transfer equation is asymmetric because the parameters of the equation vary with temperature and the Robbin boundary condition is used as well. In this paper, a three-dimensional (3D) finite difference subgridding method is proposed to simulate the electro-thermal coupling process of the multiscale circuits. The stability condition of the algorithm is deduced with a matrix method. And the efficiency and the effectiveness of the proposed subgridding approach are verified through square- and n-shaped resistances. Compared with the results of the COMSOL software and the traditional finite difference method (FDM), the proposed subgridding method has less unknowns and faster speed.

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“…However, temporal and spatial field interpolations between coarse and fine grids lead to reduced accuracy and late-time instability, especially when the grid contrast ratio is large. The Huygens subgridding method [24], [25] can achieve high accuracy for a large grid contrast ratio but its late-time instability problem still exists. The FDTD subgridding technique with separated spatial and temporal subgridding interfaces [26] can achieve higher late-time stability by carrying out the temporal and spatial interpolations separately.…”

Section: Introductionmentioning

confidence: 99%

Transformation Optics-Based Finite Difference Time Domain Algorithm for Scattering From Object With Thin Dielectric Coating

et al. 2019

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A proper dielectric coating can reduce the electromagnetic scattering of the conducting object significantly so that it cannot be detected by the radar. However, when the object contains a thin coating, fine grid size is needed to discretize the thin coating in the conventional finite-difference time-domain (FDTD) algorithm, which increases the amount of memory and computational time significantly. To overcome this dilemma, we present a transformation optics-based FDTD (TO-FDTD) algorithm to accelerate the solution of electromagnetic scattering from objects with thin dielectric coatings. Two kinds of novel TO-FDTD models are proposed in this paper for a coated cylinder and a coated arbitrary polygonal cylinder, respectively. Through coordinate transformation, the size of the object remains unchanged while its thin coating is enlarged to a thicker one, meaning that it can be simulated by the FDTD algorithm with uniform coarse grids instead of fine grids. The transformed material parameters become inhomogeneous and anisotropic in the transformed region, which can be obtained by solving a Jacobian transformation matrix. We then develop a stable FDTD algorithm for solving anisotropic Maxwell's equations. Bistatic scatterings of coated cylinders and a coated polygonal cylinder are solved by the TO-FDTD algorithm proposed in this paper, respectively. The result of the TO-FDTD algorithm matches well with the exact value and the result of the commercial software Comsol. The computational efficiency and accuracy of the proposed TO-FDTD algorithm are validated by numerical experiments. Numerical results show that the TO-FDTD algorithm has higher computational accuracy than the conventional FDTD algorithm that fails to simulate the absorbing property of the coating, when the same coarse grid size is used in the simulation. Under the same level of accuracy, the proposed TO-FDTD method can improve the computational efficiency by 62-63 times than the conventional FDTD method with fine grids in the simulations in the paper. INDEX TERMS Coated object, finite-difference time-domain (FDTD), radar cross section (RCS), transformation optics.

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Singularity Problem With the One-sheet Huygens Subgridding Method

Cited by 5 publications

References 8 publications

A Novel Transformation Optics-Based FDTD Algorithm for Fast Electromagnetic Analysis of Small Structures in a Large Scope

A Novel Transformation Optics-Based FDTD Algorithm for Fast Electromagnetic Analysis of Small Structures in a Large Scope

A Difference Subgridding Method for Solving Multiscale Electro-Thermal Problems

Transformation Optics-Based Finite Difference Time Domain Algorithm for Scattering From Object With Thin Dielectric Coating

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