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Study of FDTD and FDFD Algorithms for Electromagnetic Scattering by Complex Targets

Author: HuXiaoJuan
Tutor: GeDeBiao
School: Xi'an University of Electronic Science and Technology
Course: Radio Physics
Keywords: Electromagnetic scattering Finite-difference time-domain (FDTD) method Conformal FDTD technique Thin coating Reinforced-concrete Parallel computing for periodic structures Finite-difference frequency-domain (FDFD) method
CLC: TN011
Type: PhD thesis
Year: 2007
Downloads: 802
Quote: 5
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Based on the Yee’s cell theory that E-field samples lie on the midpoints of cells’ edges, and H-field samples on the centers of cell’s flanks in Cartesian coordinate system, a conformal finite-difference time-domain (FDTD) method based on effective constitutive parameters is presented to deal with the curved surface with magnetic or electromagnetic medium, coated targets with medium backing material or perfect electric conductor (PEC) backing material.For curved surface of medium, the effective values of permittivity and electric conductivity for E-field samples on conformal cells are calculated by weighted-length of medium and free space on the edges. The effective values of permeability and equivalent magnetic loss for H-field samples are however calculated by weighted-area of medium and free space on the flanks. The staircasing errors caused by conventional FDTD method in simulating curved surface is reduced by introducing effective constitutive parameters on the boundary of targets, and the computational precision of FDTD method is improved effectively.For a coated target with medium backing material, the CFDTD formulas about E-field and H-field samples on conformal cells are the same as those of conventional FDTD, but the constitutive parameters in CFDTD formulas are replaced by effective parameters to include the curved coating message. The effective values of permittivity and electric conductivity for E-field samples on conformal cells are calculated by weighted-length of backing medium, coating and free space. The effective values of permeability and equivalent magnetic loss for H-field samples are however calculated by weighted-area of backing medium, coating and free space. For a coated target with PEC backing material, the contour path integral is used in advance to simulate the curved PEC boundary accurately. Effective parameters are then introduced to simulate the influence of coating. The effective value of permittivity and electric conductivity for E-field samples on conformal cells are calculated by weighted-length of coating and free space, and the effective values of permeability and equivalent magnetic loss for H-field samples are however calculated by weighted-area of the coating and free space.A conformal FDTD mesh-generating scheme for coated targets base on the triangle-patch data is presented. For every vertex, the triangle-patches which have a common vertex should be figured out, and sum up all the unit external normal vector of these triangle-patches directly. The vector summation can be approximately seen as an external "average normal vector" of the common vertex. We can get a data file about the coordinates of vertexes on coating by removing the vertexes with a distance of coating thickness along their normal line, respectively. If a target is "internal coated", then vertexes should be removed along the positive direction of normal; else if it is "external coated", then vertexes should be removed along the negative direction of normal. When a target is partially coated, we only need to remove the vertexes on the coating part, and the other vertexes remain unchanged. The triangle-patches data files about the original target and coating are used to generate FDTD conformal meshes for coated target. The FDTD gridlines paralleling to the Cartesian axes x, y, z are used to penetrate coated target, and crossing-points between grid lines and triangle-patches on original target and coating are calculated by using the projection and cross-point method, respectively. These cross-points are collated according to their coordinate values. The locations of conformal meshes and the corresponding length of the edges, which are used in the conformal FDTD method, are derived by considering the coordinates and the serial number’s parity of crossing-points. Because this method can generate FDTD conformal meshes of partly or overall coated target automatically by reading the data file of the original target in the computing program, it has a strong commonality.A parallel FDTD algorithm for periodic structure on a distributed network by using the message-passing module is implemented based on the parallel platform of parallel virtual machine (PVM) system. For reinforced concrete structures, the infinite reinforced concrete layers are truncated as a single periodic unit on the basis of Floquet theory. The FDTD computational region is divided into several sub-domains along the direction that is parallel to the reinforcement meshes, and there is an overlapping region of half-cell between adjacent sub-domains for the requirement of data communication. This algorithm resolved the problems of memory insufficient and CPU-limiting of a single computer when applying the FDTD method to simulate a large-scale reinforced concrete structures. The rules of data communication and the synchronous computation between sub-domains are analyzed in detail. The speedup, efficiency in parallel computation of a concrete layer and a concrete with double layers mesh reinforcement are tested, respectively. The reflection and transmission of electromagnetic pulse penetrating typical reinforced concrete structures are analyzed systematically. A set of valuable conclusion applicable for the communication and defense engineering are obtained.The total-field/scattered-field (TF/SF) technique is studied and implemented to introduce an incident wave for the analysis of scattering problem in two- and three-dimensional finite-difference frequency-domain (FDFD) method. Based on equivalence principle, the incident wave is introduced in the total-field region by setting equivalent electromagnetic currents on the TF/SF boundary. The FDFD equations of the nodes located near the TF/SF boundary are modified to fulfill the conditions that all nodes involved belong either to the total-field or to the scattered-field. The FDFD formulas on two- and three-dimensional cases are analyzed systematically; the discrete formulas of first- and second-order Mur absorbing boundary conditions in frequency domain are discussed. The establishment and solution scheme of FDTD matrix equation is analyzed. In order to get the far field of scattering or radiating, the extrapolation schemes of Kirchhoff surface integral representation (KSIR) and equivalent electromagnetic currents are analyzed in detail. Finally, the electromagnetic scattering characters of composite targets are analyzed by using the FDFD method.

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CLC: > Industrial Technology > Radio electronics, telecommunications technology > General issues > Basic theory > Radio wave propagation,the propagation mechanism
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