Download or read book Augmented Surface Integral Equation Method for Low frequency Electromagnetic Analysis written by Zhiguo Qian and published by . This book was released on 2009 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several fundamental aspects of the surface integral equation (SIE) method including the low-frequency breakdown, the skin effect, and the substrate effect, have been addressed for full-wave electromagnetic analysis in the low-frequency regime, especially the modeling of electrical interconnects on chip and package levels. The augmentation technique is a simple and efficient remedy for the low-frequency breakdown, which is the bottleneck of the broadband simulation. Based on the augmented formulations, very complicated problems in the real world can be efficiently solved with appropriate preconditioning and fast algorithm acceleration. As required in many applications, a generalized impedance boundary condition (GIBC) formulation is developed to handle the skin effect rigorously and efficiently. It degenerates into traditional methods with two steps of approximations. These new techniques are also combined together into a comprehensive formulation to cover both the skin effect and the substrate effect without any low-frequency instability.

Download or read book Integral Equation Methods for Electromagnetic and Elastic Waves written by Weng Cho Chew and published by Morgan & Claypool Publishers. This book was released on 2009 with total page 259 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

Download or read book Fast and Well Conditioned Integral Equation Solvers for Low Frequency Electromagnetic Problems written by Qin Liu and published by . This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Fast and Well-conditioned Integral Equation Solvers for Low-frequency Electromagnetic Problems" by Qin, Liu, 刘{274b4d}, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Inspired by the important low frequency applications, such as the integrate circuits, the nano electromagnetic compatibility and quantum optics, several aspects of the computational electromagnetic low-frequency problems in surface integral equation (SIE) are carefully investigated in this dissertation. Firstly a capacitive model is studied that the convergence of the matrix system is co-determined by both the condition of the matrix and the righthand-side excitation. In a current solution, the weighted contributions from different singular vectors are not only decided by the corresponding singular values but also the right-hand side. The convergence of the capacitive problems is guaranteed by the fact that the singular vectors corresponding to the small singular values are not excited under the delta-gap source. The dominant charge currents are enough to capture the capacitive physics. Detailed spectral analysis with right-hand side effect validates the proposed theory. Secondly, in order to overcome the low-frequency inaccuracy problem for open capacitive structures in CMP-EFIE, a perturbed CMP-EFIE is proposed to extract accurate high-order current at low frequencies. Further study of the capacitive problems in CMP-EFIE utilizes a simplified two-term system by removing the contribution from the hypersingular preconditioned term, which captures the correct physics without doing the perturbation steps. The afore-built right-hand side analysis theory is applied here to explain the stability and accuracy of the simplified CMP-EFIE system. Thirdly, a point testing system is constructed to eliminate the nontrivial nullspaces of the static MFIE systems by enforcing extra zero magnetic flux conditions at the testing points locations. The projection of the current solution onto the magnetostatic nullspaces is truncated accordingly, thus the system convergence can be much improved without losing any accuracy. Finally, the electromagnetic solution is obtained from a potential-based integral equation solver, capturing electrostatic physics from the scalar potential formulation and magnetostatic physics from the vector potential formulation. The combination of the two formulations reveals the correct solution and physics at low frequencies. And the equations, formulated with the potential quantities, make it possible to couple with quantum effects theories. The resulting system appears to be a symmetric saddle point problem, where the efficiency of the iterative solver can be well-solved by a typical appropriate constraint preconditioner. The stability and capability of the new system in solving different kinds of electromagnetic problems are validated over a wide range of frequency range. The research topics in this dissertation cover different aspects of low frequency integral equation solvers, aiming at fast, stable, wide-band and accurate integral algorithms. Subjects: Integral equations Electromagnetic fields - Mathematical models

Download or read book An Enhanced Volume Integral Equation Method and Augmented Equivalence Principle Algorithm for Low Frequency Problems written by Lin Sun and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Two techniques based on integral equation methods are addressed. Firstly, a novel volume integral equation method is proposed to characterize the scattering properties of dielectric objects involving inhomogeneous and anisotropic permittivity and permeability. Two algorithms are available: conventional method of moments and reciprocity preserving method. Both of them are applied to both the permittivity and permeability terms. Curl-conforming edge elements are used to model the electric field distributions. Integration by parts is applied to deal with the singularities at the boundary introduced by the discontinuities of the material properties. Duffy's method formulations are derived for all the surface and volume singular integrations. Moreover, the multilevel fast multipole algorithm (MLFMA) is utilized to accelerate the matrix vector product process for large problems. Representative numerical results are shown to be excellent. Secondly, the present equivalence principle algorithm (EPA) is augmented by introducing charge densities as extra unknowns. This helps to separate the vector potential term and scalar potential term and avoid the imbalance at low frequencies. The current continuity constraint is enforced in both the scattering operator and translation operator. These further form a new augmented EPA equation system. With this technique, the low-frequency breakdown of EPA is removed. The augmented system serves not only as a stable low-frequency method, but also as a substitute over the whole frequency band. The new scheme is verified by numerical examples.

Download or read book The Multilevel Fast Multipole Algorithm MLFMA for Solving Large Scale Computational Electromagnetics Problems written by Ozgur Ergul and published by John Wiley & Sons. This book was released on 2014-04-22 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Multilevel Fast Multipole Algorithm (MLFMA) for Solving Large-Scale Computational Electromagnetic Problems provides a detailed and instructional overview of implementing MLFMA. The book: Presents a comprehensive treatment of the MLFMA algorithm, including basic linear algebra concepts, recent developments on the parallel computation, and a number of application examples Covers solutions of electromagnetic problems involving dielectric objects and perfectly-conducting objects Discusses applications including scattering from airborne targets, scattering from red blood cells, radiation from antennas and arrays, metamaterials etc. Is written by authors who have more than 25 years experience on the development and implementation of MLFMA The book will be useful for post-graduate students, researchers, and academics, studying in the areas of computational electromagnetics, numerical analysis, and computer science, and who would like to implement and develop rigorous simulation environments based on MLFMA.

Download or read book Advances in Time Domain Computational Electromagnetic Methods written by Qiang Ren and published by John Wiley & Sons. This book was released on 2022-11-15 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover state-of-the-art time domain electromagnetic modeling and simulation algorithms Advances in Time-Domain Computational Electromagnetic Methods delivers a thorough exploration of recent developments in time domain computational methods for solving complex electromagnetic problems. The book discuses the main time domain computational electromagnetics techniques, including finite-difference time domain (FDTD), finite-element time domain (FETD), discontinuous Galerkin time domain (DGTD), time domain integral equation (TDIE), and other methods in electromagnetic, multiphysics modeling and simulation, and antenna designs. The book bridges the gap between academic research and real engineering applications by comprehensively surveying the full picture of current state-of-the-art time domain electromagnetic simulation techniques. Among other topics, it offers readers discussions of automatic load balancing schemes for DG DG-FETD/SETD methods and convolution quadrature time domain integral equation methods for electromagnetic scattering. Advances in Time-Domain Computational Electromagnetic Methods also includes: Introductions to cylindrical, spherical, and symplectic FDTD, as well as FDTD for metasurfaces with GSTC and FDTD for nonlinear metasurfaces Explorations of FETD for dispersive and nonlinear media and SETD-DDM for periodic/quasi-periodic arrays Discussions of TDIE, including explicit marching-on-in-time solvers for second-kind time domain integral equations, TD-SIE DDM, and convolution quadrature time domain integral equation methods for electromagnetic scattering Treatments of deep learning, including time domain electromagnetic forward and inverse modeling using a differentiable programming platform Ideal for undergraduate and graduate students studying the design and development of various kinds of communication systems, as well as professionals working in these fields, Advances in Time-Domain Computational Electromagnetic Methods is also an invaluable resource for those taking advanced graduate courses in computational electromagnetic methods and simulation techniques.

Download or read book Integral Equations for Real Life Multiscale Electromagnetic Problems written by Francesca Vipiana and published by IET. This book was released on 2024-01-09 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compiled by two editors with substantial experience in developing algorithms to numerically solve integral equations in the case of discretized real-life structures, this book explains the main available approaches for the numerical solution of surface integral equations for analysing real-world multi-scale electromagnetic problems.

Download or read book Reduced order Integral Equation Methods to Solve Complex Electromagnetic Problems written by Utkarsh Patel and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite vast advancements in computational hardware capabilities, full-wave electromagnetic simulations of many multiscale problems continue to be a daunting task. Multiscale problems are encountered, for example, when modeling interconnects in an integrated circuit or when simulating complex electromagnetic structures. In interconnect problems, the main challenge is to model the multiscale skin effect that develops inside the conductors at high frequency. Similarly, complex electromagnetic structures are multiscale because these surfaces are tens of wavelengths large, while each unit cell often contains subwavelength geometrical features. This thesis presents reduced-order integral equation methods to solve complex multiscale problems. For interconnect problems, it proposes a single-source surface integral equation method to model 2-D and 3-D conductors or dielectrics of arbitrary shape. In this approach, electromagnetic fields inside a conductor or a dielectric object are accurately modeled by a differential surface admittance operator and an equivalent electric current density on the object's surface. Since the proposed method does not use any volumetric unknowns, it is more efficient than volumetric methods encountered in the literature and commercial solvers, which require a fine mesh to model the skin effect. Furthermore, since the proposed approach is single-source, it is more efficient than other surface methods in the literature that require both equivalent electric and magnetic current densities. Numerical results show that the proposed method can be over 100x and 20x faster than commercial FEM solvers for 2-D and 3-D problems, respectively, while consuming significantly lower memory. The proposed surface method for conductors and dielectrics is further generalized to develop the so-called macromodeling technique to simulate complex scatterers. In this technique, a heterogeneous scatterer composed of dielectric and PEC objects is accurately modeled by equivalent electric and magnetic current densities that are introduced on a fictitious surface enclosing the element. The crux of the technique is to solve for unknowns only on the fictitious surface, instead of the scatterers, which results in fewer unknowns. Numerical results show that the proposed macromodeling technique can efficiently simulate electrically large reflectarrays composed of square patches and Jerusalem crosses, that are difficult to simulate even with commercial solvers.

Download or read book Integral Equation Techniques in Transient Electromagnetics written by Dragan Poljak and published by Computational Mechanics. This book was released on 2003 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transient electromagnetic phenomena can be treated in two ways, either using direct time domain modeling or frequency domain analysis applying the inverse Fourier transform. Both approaches are important since each has distinct advantages depending on the situation or the application.

Download or read book Parallel Algorithms in Computational Science and Engineering written by Ananth Grama and published by Springer Nature. This book was released on 2020-07-06 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume highlights two areas of fundamental interest in high-performance computing: core algorithms for important kernels and computationally demanding applications. The first few chapters explore algorithms, numerical techniques, and their parallel formulations for a variety of kernels that arise in applications. The rest of the volume focuses on state-of-the-art applications from diverse domains. By structuring the volume around these two areas, it presents a comprehensive view of the application landscape for high-performance computing, while also enabling readers to develop new applications using the kernels. Readers will learn how to choose the most suitable parallel algorithms for any given application, ensuring that theory and practicality are clearly connected. Applications using these techniques are illustrated in detail, including: Computational materials science and engineering Computational cardiovascular analysis Multiscale analysis of wind turbines and turbomachinery Weather forecasting Machine learning techniques Parallel Algorithms in Computational Science and Engineering will be an ideal reference for applied mathematicians, engineers, computer scientists, and other researchers who utilize high-performance computing in their work.

Download or read book Boundary Integral Equations written by George C. Hsiao and published by Springer Nature. This book was released on 2021-03-26 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of the book which has two additional new chapters on Maxwell’s equations as well as a section on properties of solution spaces of Maxwell’s equations and their trace spaces. These two new chapters, which summarize the most up-to-date results in the literature for the Maxwell’s equations, are sufficient enough to serve as a self-contained introductory book on the modern mathematical theory of boundary integral equations in electromagnetics. The book now contains 12 chapters and is divided into two parts. The first six chapters present modern mathematical theory of boundary integral equations that arise in fundamental problems in continuum mechanics and electromagnetics based on the approach of variational formulations of the equations. The second six chapters present an introduction to basic classical theory of the pseudo-differential operators. The aforementioned corresponding boundary integral operators can now be recast as pseudo-differential operators. These serve as concrete examples that illustrate the basic ideas of how one may apply the theory of pseudo-differential operators and their calculus to obtain additional properties for the corresponding boundary integral operators. These two different approaches are complementary to each other. Both serve as the mathematical foundation of the boundary element methods, which have become extremely popular and efficient computational tools for boundary problems in applications. This book contains a wide spectrum of boundary integral equations arising in fundamental problems in continuum mechanics and electromagnetics. The book is a major scholarly contribution to the modern approaches of boundary integral equations, and should be accessible and useful to a large community of advanced graduate students and researchers in mathematics, physics, and engineering.

Download or read book Fast and Well conditioned Integral Equation Solvers for Low frequency Electromagnetic Problems written by 刘{274b4d} (Researcher on electrical and electronic engineering) and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fast and Well conditioned Integral Equation Solvers for Low frequency Electromagnetic Problems written by 刘琴 and published by . This book was released on 2015 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book FFT and Multigrid Accelerated Integral Equation Solvers for Multi scale Electromagnetic Analysis in Complex Backgrounds written by Kai Yang and published by . This book was released on 2014 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Novel integral-equation methods for efficiently solving electromagnetic problems that involve more than a single length scale of interest in complex backgrounds are presented. Such multi-scale electromagnetic problems arise because of the interplay of two distinct factors: the structure under study and the background medium. Both can contain material properties (wavelengths/skin depths) and geometrical features at different length scales, which gives rise to four types of multi-scale problems: (1) twoscale, (2) multi-scale structure, (3) multi-scale background, and (4) multi-scale-squared problems, where a single-scale structure resides in a different single-scale background, a multi-scale structure resides in a single-scale background, a single-scale structure resides in a multi-scale background, and a multi-scale structure resides in a multi-scale background, respectively. Electromagnetic problems can be further categorized in terms of the relative values of the length scales that characterize the structure and the background medium as (a) high-frequency, (b) low-frequency, and (c) mixed-frequency problems, where the wavelengths/skin depths in the background medium, the structure's geometrical features or internal wavelengths/skin depths, and a combination of these three factors dictate the field variations on/in the structure, respectively. This dissertation presents several problems arising from geophysical exploration and microwave chemistry that demonstrate the different types of multi-scale problems encountered in electromagnetic analysis and the computational challenges they pose. It also presents novel frequency-domain integral-equation methods with proper Green function kernels for solving these multi-scale problems. These methods avoid meshing the background medium and finding fields in an extended computational domain outside the structure, thereby resolving important complications encountered in type 3 and 4 multi-scale problems that limit alternative methods. Nevertheless, they have been of limited practical use because of their high computational costs and because most of the existing 'fast integral-equation algorithms' are not applicable to complex Green function kernels. This dissertation introduces novel FFT, multigrid, and FFT-truncated multigrid algorithms that reduce the computational costs of frequency-domain integral-equation methods for complex backgrounds and enable the solution of unprecedented type 3 and 4 multi-scale problems. The proposed algorithms are formulated in detail, their computational costs are analyzed theoretically, and their features are demonstrated by solving benchmark and challenging multi-scale problems.

Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1156 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: