Electromagnetic Scattering Using The Iterative Multi Region Technique

In this work, an iterative approach using the finite difference frequency domain method is presented to solve the problem of scattering from large-scale electromagnetic structures. The idea of the proposed iterative approach is to divide one computational domain into smaller subregions and solve each subregion separately. Then the subregion solutions are combined iteratively to obtain a solution for the complete domain. As a result, a considerable reduction in the computation time and memory is achieved. This procedure is referred to as the iterative multiregion (IMR) technique. Different enhancement procedures are investigated and introduced toward the construction of this technique. These procedures are the following: 1) a hybrid technique combining the IMR technique and a method of moment technique is found to be efficient in producing accurate results with a remarkable computer memory saving; 2) the IMR technique is implemented on a parallel platform that led to a tremendous computational time saving; 3) together, the multigrid technique and the incomplete lower and upper preconditioner are used with the IMR technique to speed up the convergence rate of the final solution, which reduces the total computational time. Thus, the proposed iterative technique, in conjunction with the enhancement procedures, introduces a novel approach to solving large open-boundary electromagnetic problems including unconnected objects in an efficient and robust way. Contents: Basics of the FDFD Method / IMR Technique for Large-Scale Electromagnetic Scattering Problems: 3D Case / IMR Technique for Large-Scale Electromagnetic Scattering Problems: 2D Case / The IMR Algorithm Using a Hybrid FDFD and Method of Moments Technique / Parallelization of the Iterative Multiregion Technique / Combined Multigrid Technique and IMR Algorithm / Concluding Remarks / Appendices

In this work, an iterative approach using the finite difference frequency domain method is presented to solve the problem of scattering from large-scale electromagnetic structures. The idea of the proposed iterative approach is to divide one computational domain into smaller subregions and solve each subregion separately. Then the subregion solutions are combined iteratively to obtain a solution for the complete domain. As a result, a considerable reduction in the computation time and memory is achieved. This procedure is referred to as the iterative multiregion (IMR) technique. Different enhancement procedures are investigated and introduced toward the construction of this technique. These procedures are the following: 1) a hybrid technique combining the IMR technique and a method of moment technique is found to be efficient in producing accurate results with a remarkable computer memory saving; 2) the IMR technique is implemented on a parallel platform that led to a tremendous computational time saving; 3) together, the multigrid technique and the incomplete lower and upper preconditioner are used with the IMR technique to speed up the convergence rate of the final solution, which reduces the total computational time. Thus, the proposed iterative technique, in conjunction with the enhancement procedures, introduces a novel approach to solving large open-boundary electromagnetic problems including unconnected objects in an efficient and robust way.

In this work, an iterative approach using the finite difference frequency domain method is presented to solve the problem of scattering from large-scale electromagnetic structures. The idea of the proposed iterative approach is to divide one computational domain into smaller subregions and solve each subregion separately. Then the subregion solutions are combined iteratively to obtain a solution for the complete domain. As a result, a considerable reduction in the computation time and memory is achieved. This procedure is referred to as the iterative multiregion (IMR) technique.

This book presents the application of the overlapping grids approach to solve chiral material problems using the FDFD method. Due to the two grids being used in the technique, we will name this method as Double-Grid Finite Difference Frequency-Domain (DG-FDFD) method. As a result of this new approach the electric and magnetic field components are defined at every node in the computation space. Thus, there is no need to perform averaging during the calculations as in the aforementioned FDFD technique [16]. We formulate general 3D frequency-domain numerical methods based on double-grid (DG-FDFD) approach for general bianisotropic materials. The validity of the derived formulations for different scattering problems has been shown by comparing the obtained results to exact and other solutions obtained using different numerical methods. Table of Contents: Introduction / Chiral Media / Basics of the Finite-Difference Frequency-Domain (FDFD) Method / The Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Bianisotropic Medium / Scattering FromThree Dimensional Chiral Structures / ImprovingTime and Memory Efficiencies of FDFD Methods / Conclusions / Appendix A: Notations / Appendix B: Near to Far FieldTransformation

In this book, a general frequency domain numerical method similar to the finite difference frequency domain (FDFD) technique is presented. The proposed method, called the multiresolution frequency domain (MRFD) technique, is based on orthogonal Battle-Lemarie and biorthogonal Cohen-Daubechies-Feauveau (CDF) wavelets. The objective of developing this new technique is to achieve a frequency domain scheme which exhibits improved computational efficiency figures compared to the traditional FDFD method: reduced memory and simulation time requirements while retaining numerical accuracy. The newly introduced MRFD scheme is successfully applied to the analysis of a number of electromagnetic problems, such as computation of resonance frequencies of one and three dimensional resonators, analysis of propagation characteristics of general guided wave structures, and electromagnetic scattering from two dimensional dielectric objects. The efficiency characteristics of MRFD techniques based on different wavelets are compared to each other and that of the FDFD method. Results indicate that the MRFD techniques provide substantial savings in terms of execution time and memory requirements, compared to the traditional FDFD method. Table of Contents: Introduction / Basics of the Finite Difference Method and Multiresolution Analysis / Formulation of the Multiresolution Frequency Domain Schemes / Application of MRFD Formulation to Closed Space Structures / Application of MRFD Formulation to Open Space Structures / A Multiresolution Frequency Domain Formulation for Inhomogeneous Media / Conclusion

In recent years, transmitarray antennas have attracted growing interest with many antenna researchers. Transmitarrays combines both optical and antenna array theory, leading to a low profile design with high gain, high radiation efficiency, and versatile radiation performance for many wireless communication systems. In this book, comprehensive analysis, new methodologies, and novel designs of transmitarray antennas are presented. Detailed analysis for the design of planar space-fed array antennas is presented. The basics of aperture field distribution and the analysis of the array elements are described. The radiation performances (directivity and gain) are discussed using array theory approach, and the impacts of element phase errors are demonstrated. The performance of transmitarray design using multilayer frequency selective surfaces (M-FSS) approach is carefully studied, and the transmission phase limit which are generally independent from the selection of a specific element shape is revealed. The maximum transmission phase range is determined based on the number of layers, substrate permittivity, and the separations between layers. In order to reduce the transmitarray design complexity and cost, three different methods have been investigated. As a result, one design is performed using quad-layer cross-slot elements with no dielectric material and another using triple-layer spiral dipole elements. Both designs were fabricated and tested at X-Band for deep space communications. Furthermore, the radiation pattern characteristics were studied under different feed polarization conditions and oblique angles of incident field from the feed. New design methodologies are proposed to improve the bandwidth of transmitarray antennas through the control of the transmission phase range of the elements. These design techniques are validated through the fabrication and testing of two quad-layer transmitarray antennas at Ku-band. A single-feed quad-beam transmitarray antenna with 50 degrees elevation separation between the beams is investigated, designed, fabricated, and tested at Ku-band. In summary, various challenges in the analysis and design of transmitarray antennas are addressed in this book. New methodologies to improve the bandwidth of transmitarray antennas have been demonstrated. Several prototypes have been fabricated and tested, demonstrating the desirable features and potential new applications of transmitarray antennas.

This book is a self-contained, programming-oriented and learner-centered book on finite element method (FEM), with special emphasis given to developing MATLAB® programs for numerical modeling of electromagnetic boundary value problems. It provides a deep understanding and intuition of FEM programming by means of step-by-step MATLAB® programs with detailed descriptions, and eventually enabling the readers to modify, adapt and apply the provided programs and formulations to develop FEM codes for similar problems through various exercises. It starts with simple one-dimensional static and time-harmonic problems and extends the developed theory to more complex two- or three-dimensional problems. It supplies sufficient theoretical background on the topic, and it thoroughly covers all phases (pre-processing, main body and post-processing) in FEM. FEM formulations are obtained for boundary value problems governed by a partial differential equation that is expressed in terms of a generic unknown function, and then, these formulations are specialized to various electromagnetic applications together with a post-processing phase. Since the method is mostly described in a general context, readers from other disciplines can also use this book and easily adapt the provided codes to their engineering problems. After forming a solid background on the fundamentals of FEM by means of canonical problems, readers are guided to more advanced applications of FEM in electromagnetics through a survey chapter at the end of the book. Offers a self-contained and easy-to-understand introduction to the theory and programming of finite element method. Covers various applications in the field of static and time-harmonic electromagnetics. Includes one-, two- and three-dimensional finite element codes in MATLAB®. Enables readers to develop finite element programming skills through various MATLAB® codes and exercises. Promotes self-directed learning skills and provides an effective instruction tool.