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A Combination Of Rao Wilton Glisson And Asymptotic Phase Basis Functions To Solve The Electric And Magnetic Field Integral Equations
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Book Synopsis A Combination of Rao-Wilton-Glisson and Asymptotic Phase Basis Functions to Solve the Electric and Magnetic Field Integral Equations by : John Robert Gulick
Download or read book A Combination of Rao-Wilton-Glisson and Asymptotic Phase Basis Functions to Solve the Electric and Magnetic Field Integral Equations written by John Robert Gulick and published by . This book was released on 2001 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using the method of moments to solve the electric and magnetic field integral equations for the currents on a PEC surface requires a large number of unknowns to capture the current's rapid spatial variation across the surface. Rao-Wilton-Glisson (RWG) vector basis functions 1 have been successfully used for the past twenty years 1, 2, 3,.... Unfortunately, the required number of unknowns is on the order of 100 per square wavelength making electrically large problems impractical. For large smooth objects, the rapid spatial variation in the current is due to phase variations rather than magnitude variations. Thus, using asymptotic phase (AP) basis functions can drastically reduce the number of unknowns 3 for large, smooth metallic bodies. The A') basis flinction incorporates the anticipated phase, hence represents a more efficient basis function for a large class of problems. However, using RWG basis functions for monostatic calculations is more efficient since the matrix entries need not be recomputed for each new incidence angle, as is the case for an AP expansion. One can combine the methods; selecting RWG or AP basis functions for a given geometry based on an element's location within the geometry. This allows the relaxation of mesh density in smooth flat regions not near the discontinuities resulting in a significant reduction of unknowns. This research shows that combining functions is highly efficient and the effectiveness of this method depends on the geometry of application.
Book Synopsis Electrical & Electronics Abstracts by :
Download or read book Electrical & Electronics Abstracts written by and published by . This book was released on 1997 with total page 1860 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Digest by : IEEE Antennas and Propagation Society. International Symposium
Download or read book Digest written by IEEE Antennas and Propagation Society. International Symposium and published by . This book was released on 2002 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Low Order-singularity Electric-field Integral Equation Solvable with Pulse Basis Functions and Point Matching by : Robert A. Shore
Download or read book A Low Order-singularity Electric-field Integral Equation Solvable with Pulse Basis Functions and Point Matching written by Robert A. Shore and published by . This book was released on 2005 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integral Equations and Iteration Methods in Electromagnetic Scattering by : A. B. Samokhin
Download or read book Integral Equations and Iteration Methods in Electromagnetic Scattering written by A. B. Samokhin and published by Walter de Gruyter. This book was released on 2013-03-12 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Phase-integral Methods by : John Heading
Download or read book An Introduction to Phase-integral Methods written by John Heading and published by . This book was released on 1962 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Augmented Electric and Magnetic-field Integral Equations by : Arthur D. Yaghjian
Download or read book Augmented Electric and Magnetic-field Integral Equations written by Arthur D. Yaghjian and published by . This book was released on 1981 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integral Equation Methods for Electromagnetic and Elastic Waves by : Weng Chew
Download or read book Integral Equation Methods for Electromagnetic and Elastic Waves written by Weng Chew and published by Springer Nature. This book was released on 2022-05-31 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners. Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) due to increased computing power. The interest in this area was on the wane when it was demonstrated that differential equation methods, with their sparse matrices, can solve many problems more efficiently than integral equation methods. Recently, due to the advent of fast algorithms, there has been a revival in integral equation methods in electromagnetics. Much of our work in recent years has been in fast algorithms for integral equations, which prompted our interest in integral equation methods. While previously, only tens of thousands of unknowns could be solved by integral equation methods, now, tens of millions of unknowns can be solved with fast algorithms. This has prompted new enthusiasm in integral equation methods. Table of Contents: Introduction to Computational Electromagnetics / Linear Vector Space, Reciprocity, and Energy Conservation / Introduction to Integral Equations / Integral Equations for Penetrable Objects / Low-Frequency Problems in Integral Equations / Dyadic Green's Function for Layered Media and Integral Equations / Fast Inhomogeneous Plane Wave Algorithm for Layered Media / Electromagnetic Wave versus Elastic Wave / Glossary of Acronyms
Book Synopsis Time Domain Boundary Integral Equations Analysis by : Amir Geranmayeh
Download or read book Time Domain Boundary Integral Equations Analysis written by Amir Geranmayeh and published by Sudwestdeutscher Verlag Fur Hochschulschriften AG. This book was released on 2011-01 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present research study mainly involves a survey of diverse time-domain boundary element methods that can be used to numerically solve the retarded potential integral equations. The aim is to address the late-time stability, accuracy, and computational complexity concerns in time-domain surface integral equation approaches. The study generally targets the transient electromagnetic scattering of three- dimensional perfectly conducting bodies. Efficient algorithms are developed to numerically solve the electric, magnetic, and combined field integral equations for the unknown induced surface current. The algorithms are mainly categorized into three major discretization schemes, namely the marching-on- in-time, the marching-on-in-order, and the convolution quadrature methods or finite difference delay modeling. Possible choices of space-time integration are examined and the results are compared with the finite integration technique's solution. The outcome is applied to the non- dispersive modeling of the field propagation in particle accelerator structures, when travelling bunches of charged particles passes through the beam line elements.
Book Synopsis Projective Solution of Integral Equations Arising in Electric and Magnetic Field Problems by : Peter P. Silvester
Download or read book Projective Solution of Integral Equations Arising in Electric and Magnetic Field Problems written by Peter P. Silvester and published by . This book was released on 1970 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many integral equations arising in electric and magnetic field problems have Green's function kernels, which cause difficulty in integration because of their essential singularities. By performing a simple coordinate rotation, these singularities can be shifted entirely onto one coordinate axis, so that iterated weighted numerical quadratures may be applied to evaluate exactly the projective representation of such integral operators on suitable finite-dimensional function spaces. Standard projective methods may therefore be applied to solve such integral equations accurately with very little computational effort. (Author).
Book Synopsis Evaluation of Singular Electric Field Integral Equation (EFIE) Matrix Elements by :
Download or read book Evaluation of Singular Electric Field Integral Equation (EFIE) Matrix Elements written by and published by . This book was released on 2001 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The electric field integral equation (EFIE) solution for scattering from an arbitrary three-dimensional geometry was published by Rao, Wilton, and Glisson (RWG) in 1982. For electrically large problems, with large systems of equations, the physical fidelity of the solution can be improved with increased numerical accuracy of the Galerkin inner products which populate the method of moments (MoM) impedance matrix. A new treatment of these inner products is presented here which improves the accuracy of the singular surface integrals that result from the Galerkin formulation.
Book Synopsis The Method of Moments in Electromagnetics by : Walton C. Gibson
Download or read book The Method of Moments in Electromagnetics written by Walton C. Gibson and published by CRC Press. This book was released on 2021-09-06 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Method of Moments in Electromagnetics, Third Edition details the numerical solution of electromagnetic integral equations via the Method of Moments (MoM). Previous editions focused on the solution of radiation and scattering problems involving conducting, dielectric, and composite objects. This new edition adds a significant amount of material on new, state-of-the art compressive techniques. Included are new chapters on the Adaptive Cross Approximation (ACA) and Multi-Level Adaptive Cross Approximation (MLACA), advanced algorithms that permit a direct solution of the MoM linear system via LU decomposition in compressed form. Significant attention is paid to parallel software implementation of these methods on traditional central processing units (CPUs) as well as new, high performance graphics processing units (GPUs). Existing material on the Fast Multipole Method (FMM) and Multi-Level Fast Multipole Algorithm (MLFMA) is also updated, blending in elements of the ACA algorithm to further reduce their memory demands. The Method of Moments in Electromagnetics is intended for students, researchers, and industry experts working in the area of computational electromagnetics (CEM) and the MoM. Providing a bridge between theory and software implementation, the book incorporates significant background material, while presenting practical, nuts-and-bolts implementation details. It first derives a generalized set of surface integral equations used to treat electromagnetic radiation and scattering problems, for objects comprising conducting and dielectric regions. Subsequent chapters apply these integral equations for progressively more difficult problems such as thin wires, bodies of revolution, and two- and three-dimensional bodies. Radiation and scattering problems of many different types are considered, with numerical results compared against analytical theory as well as measurements.
Book Synopsis Acceleration Methods of Discontinuous Galerkin Integral Equation for Maxwell's Equations by : Chung Hyun Lee (Electric engineer)
Download or read book Acceleration Methods of Discontinuous Galerkin Integral Equation for Maxwell's Equations written by Chung Hyun Lee (Electric engineer) and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, the discontinuous Galerkin integral equation (IEDG) method has been introduced in the computational electromagnetic community. This method can be helpful for mesh preparation because of the guaranteed flexibility of the geometry and the basis functions. However, this method has the intrinsic drawback that additional integral terms are required during integration by parts, hence potentially increasing the computational cost. In addition, because this method is relatively new, it is not yet an active focus of research, despite its obvious advantages. Therefore, in this article, three different methods for accelerating the IEDG method are proposed using the unique characteristics of the method itself. Similar to other partial differential equation methods, the IEDG method can be divided into three basic stages: computation of the impedance matrix using the IEDG formulation, preparation of the right-hand side (RHS) matrix for multiple angular responses, and solution of the matrix equations with iterative solvers. Accordingly, a different method is proposed for each stage of the IEDG process. For the first stage, a new procedure for efficient numerical integration is presented based on the fact that each integration term can be divided into three submatrices that are universally used for entire elements, can be stored in advance for each patch, and are related to two source and field elements. Because those matrices can also be shared between integration terms, one can take advantage of this to achieve the acceleration of numerical integration. In addition, approximation by the impedance boundary condition (IBC) in the IEDG framework can also be easily formulated with the proposed numerical integration method. Second, based on rigorous error analysis, an efficient and error-controllable angular sweep algorithm is proposed. With this algorithm, the solution process can be accelerated based on two factors: only a minimum set of singular vectors can be stored for the solution process, and the tolerance of the iterative solver for each singular vector can be mitigated. It is proven that two types of bounded numerical errors arise: the solution error computed based on the vector-induced matrix norm and the root mean square (RMS) of the solution errors for individual RHS vectors. In addition, a block version of the generalized conjugate residual (GCR) is proposed to accelerate the solution process with a limited increase in memory. For various targets of different sizes and materials, the above errors and accelerations are numerically validated. Finally, a robust preconditioner for accelerating the Krylov subspace method is presented, which is constructed by stacking two preconditioners to alleviate different physical problems. The first is the near-field preconditioner, which is the inverse of a sparse matrix consisting only of interactions within a predetermined distance. Nested dissection reordering is used to conserve memory and time for factorization. In addition, a global preconditioner is stacked on top of the near-field preconditioner to enhance the robustness. The global preconditioner is based on the approximate inverse of the summation matrix of the identity matrix and off-diagonal terms. Principal component analysis (PCA) and the Sherman-Morrison-Woodbury formula are used to obtain the inverse. Additionally, the transpose of the multilevel fast multipole method is described, along with numerical validations, since left vector-matrix multiplication is required to implement the PCA process. Finally, the deflation technique is used for the further acceleration of iterative solvers.
Book Synopsis Integral Equation Methods for Electromagnetics by : Nagayoshi Morita
Download or read book Integral Equation Methods for Electromagnetics written by Nagayoshi Morita and published by . This book was released on 1990-01-01 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Functional Analysis: Entering Hilbert Space (Second Edition) by : Vagn Lundsgaard Hansen
Download or read book Functional Analysis: Entering Hilbert Space (Second Edition) written by Vagn Lundsgaard Hansen and published by World Scientific Publishing Company. This book was released on 2015-12-01 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbert spaces. It exhibits a construction of the space of pth power Lebesgue integrable functions by a completion procedure with respect to a suitable norm in a space of continuous functions, including proofs of the basic inequalities of Hölder and Minkowski. The Lp-spaces thereby emerges in direct analogy with a construction of the real numbers from the rational numbers. This allows grasping the main ideas more rapidly. Other important Banach spaces arising from function spaces and sequence spaces are also treated.In this second edition, I have expanded the material on normed vector spaces and their operators presented in Chapter 1 to include proofs of the Open Mapping Theorem, the Closed Graph Theorem and the Hahn-Banach Theorem. The material on operators between normed vector spaces is further expanded in a new Chapter 6, which presents the basic elements of the theory of Fredholm operators on general Banach spaces, not only on Hilbert spaces. This requires that we develop the theory of dual operators between Banach spaces to replace the use of adjoint operators between Hilbert spaces.With the addition of the new material on normed vector spaces and their operators, the book can serve as a general introduction to functional analysis viewed as a theory of infinite dimensional linear spaces and linear operators acting on them.
Book Synopsis An Introduction to the Locally Corrected Nystrom Method by : Andrew Peterson
Download or read book An Introduction to the Locally Corrected Nystrom Method written by Andrew Peterson and published by Springer. This book was released on 2009-11-06 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lecture provides a tutorial introduction to the Nyström and locally-corrected Nyström methods when used for the numerical solutions of the common integral equations of two-dimensional electromagnetic fields. These equations exhibit kernel singularities that complicate their numerical solution. Classical and generalized Gaussian quadrature rules are reviewed. The traditional Nyström method is summarized, and applied to the magnetic field equation for illustration. To obtain high order accuracy in the numerical results, the locally-corrected Nyström method is developed and applied to both the electric field and magnetic field equations. In the presence of target edges, where current or charge density singularities occur, the method must be extended through the use of appropriate singular basis functions and special quadrature rules. This extension is also described. Table of Contents: Introduction / Classical Quadrature Rules / The Classical Nyström Method / The Locally-Corrected Nyström Method / Generalized Gaussian Quadrature / LCN Treatment of Edge Singularities
Book Synopsis Fundamentals of the Physical Theory of Diffraction by : Pyotr Ya. Ufimtsev
Download or read book Fundamentals of the Physical Theory of Diffraction written by Pyotr Ya. Ufimtsev and published by John Wiley & Sons. This book was released on 2007-02-09 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first complete and comprehensive description of the modern Physical Theory of Diffraction (PTD) based on the concept of elementary edge waves (EEWs). The theory is demonstrated with the example of the diffraction of acoustic and electromagnetic waves at perfectly reflecting objects. The derived analytic expressions clearly explain the physical structure of the scattered field and describe in detail all of the reflected and diffracted rays and beams, as well as the fields in the vicinity of caustics and foci. Shadow radiation, a new fundamental component of the field, is introduced and proven to contain half of the total scattered power.
