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Author: Vladimir Rohklin Publisher: ISBN: Category : Languages : en Pages : 74
Book Description
During the existence of the project, we designed Fast Multipole algorithms for the solution of the Laplace and Helmholtz equations, the latter predominately in the low-frequency regime. The principal analytical apparatus used were the new diagonal forms of translation operators for the Laplace and Helmholtz equation; such diagonal forms in turn required the use of Generalized Gaussian Quadratures, which we have also designed. In addition, we redesigned the logical structure of such algorithms, drastically reducing their memory requirements. At the present time, extremely efficient Fast Multipole Methods for the Laplace equation in three dimensions are in existence; the construction of such schemes for the Helmholtz equation in the low-frequency regime has been reduced to a purely programming task. Six publications reporting this work have appeared (or been accepted) in refereed journals; two publications have been released in the report form, and are about to be submitted to refereed journals; three publications are in preparation.
Author: Vladimir Rohklin Publisher: ISBN: Category : Languages : en Pages : 74
Book Description
During the existence of the project, we designed Fast Multipole algorithms for the solution of the Laplace and Helmholtz equations, the latter predominately in the low-frequency regime. The principal analytical apparatus used were the new diagonal forms of translation operators for the Laplace and Helmholtz equation; such diagonal forms in turn required the use of Generalized Gaussian Quadratures, which we have also designed. In addition, we redesigned the logical structure of such algorithms, drastically reducing their memory requirements. At the present time, extremely efficient Fast Multipole Methods for the Laplace equation in three dimensions are in existence; the construction of such schemes for the Helmholtz equation in the low-frequency regime has been reduced to a purely programming task. Six publications reporting this work have appeared (or been accepted) in refereed journals; two publications have been released in the report form, and are about to be submitted to refereed journals; three publications are in preparation.
Author: Jian-Ming Jin Publisher: John Wiley & Sons ISBN: 1119108098 Category : Science Languages : en Pages : 756
Book Description
Reviews the fundamental concepts behind the theory and computation of electromagnetic fields The book is divided in two parts. The first part covers both fundamental theories (such as vector analysis, Maxwell’s equations, boundary condition, and transmission line theory) and advanced topics (such as wave transformation, addition theorems, and fields in layered media) in order to benefit students at all levels. The second part of the book covers the major computational methods for numerical analysis of electromagnetic fields for engineering applications. These methods include the three fundamental approaches for numerical analysis of electromagnetic fields: the finite difference method (the finite difference time-domain method in particular), the finite element method, and the integral equation-based moment method. The second part also examines fast algorithms for solving integral equations and hybrid techniques that combine different numerical methods to seek more efficient solutions of complicated electromagnetic problems. Theory and Computation of Electromagnetic Fields, Second Edition: Provides the foundation necessary for graduate students to learn and understand more advanced topics Discusses electromagnetic analysis in rectangular, cylindrical and spherical coordinates Covers computational electromagnetics in both frequency and time domains Includes new and updated homework problems and examples Theory and Computation of Electromagnetic Fields, Second Edition is written for advanced undergraduate and graduate level electrical engineering students. This book can also be used as a reference for professional engineers interested in learning about analysis and computation skills.
Author: Raj Mittra Publisher: Springer Science & Business Media ISBN: 1461443822 Category : Technology & Engineering Languages : en Pages : 707
Book Description
Emerging Topics in Computational Electromagnetics in Computational Electromagnetics presents advances in Computational Electromagnetics. This book is designed to fill the existing gap in current CEM literature that only cover the conventional numerical techniques for solving traditional EM problems. The book examines new algorithms, and applications of these algorithms for solving problems of current interest that are not readily amenable to efficient treatment by using the existing techniques. The authors discuss solution techniques for problems arising in nanotechnology, bioEM, metamaterials, as well as multiscale problems. They present techniques that utilize recent advances in computer technology, such as parallel architectures, and the increasing need to solve large and complex problems in a time efficient manner by using highly scalable algorithms.
Author: Nail A Gumerov Publisher: Elsevier ISBN: 0080531598 Category : Mathematics Languages : en Pages : 551
Book Description
This volume in the Elsevier Series in Electromagnetism presents a detailed, in-depth and self-contained treatment of the Fast Multipole Method and its applications to the solution of the Helmholtz equation in three dimensions. The Fast Multipole Method was pioneered by Rokhlin and Greengard in 1987 and has enjoyed a dramatic development and recognition during the past two decades. This method has been described as one of the best 10 algorithms of the 20th century. Thus, it is becoming increasingly important to give a detailed exposition of the Fast Multipole Method that will be accessible to a broad audience of researchers. This is exactly what the authors of this book have accomplished. For this reason, it will be a valuable reference for a broad audience of engineers, physicists and applied mathematicians. The Only book that provides comprehensive coverage of this topic in one location Presents a review of the basic theory of expansions of the Helmholtz equation solutions Comprehensive description of both mathematical and practical aspects of the fast multipole method and it's applications to issues described by the Helmholtz equation
Author: Wenhua Yu Publisher: Artech House ISBN: 1608078973 Category : Technology & Engineering Languages : en Pages : 597
Book Description
This new resource covers the latest developments in computational electromagnetic methods, with emphasis on cutting-edge applications. This book is designed to extend existing literature to the latest development in computational electromagnetic methods, which are of interest to readers in both academic and industrial areas. The topics include advanced techniques in MoM, FEM and FDTD, spectral domain method, GPU and Phi hardware acceleration, metamaterials, frequency and time domain integral equations, and statistics methods in bio-electromagnetics.
Author: Leopold B. Felsen Publisher: Springer Science & Business Media ISBN: 3540939466 Category : Technology & Engineering Languages : en Pages : 219
Book Description
In this monograph, the authors propose a systematic and rigorous treatment of electromagnetic field representations in complex structures. The architecture suggested in this book accommodates use of different numerical methods as well as alternative Green's function representations in each of the subdomains resulting from a partitioning of the overall problem. The subdomains are regions of space where electromagnetic energy is stored and are described in terms of equivalent circuit representations based either on lumped element circuits or on transmission lines. Connection networks connect the subcircuits representing the subdomains. The connection networks are lossless, don't store energy and represent the overall problem topology. This is similar to what is done in circuit theory and permits a phrasing of the solution of EM field problems in complex structures by Network-oriented methods.
Author: Publisher: ISBN: Category : Languages : en Pages : 19
Book Description
In recent years, a variety of computational schemes have been developed that accelerate the iterative solution of the dense matrix equations that arise upon discretizing boundary integral equations pertinent to the description of electromagnetic scattering problems. These schemes largely fall into two categories: (i) fast multipole methods and (ii) wavelet/multiresolution schemes. The overall goal of this project is to develop and catalogue all practical hybrids between fast multipole solvers and multiresolution schemes useful to the analysis of electromagnetic boundary value problems. To this end, we developed (i) hybrid plane wave time domain (PWTD) multiresolution schemes pertinent to the construction of PWTD schemes for lossy media, (ii) PWTD schemes for 2D environments, (iii) PWTD solvers for microstrip structures, (iv) PWTD schemes for low-frequency solvers, (v) PWTD schemes for quasi-planar environments, (vi) PWTD schemes for periodic kernels, (vii) Time-Domain Adaptive Integral (TD-AIM) kernels for solving timedomain integral equations, (viii) TD-AIM accelerated hybrid time domain integral equation SPICE based circuit solvers, and (ix) a novel multigrid accelerator for the full wave finite element analysis of electromagnetic phenomena. Each and every of these solvers uses a multiresolution framework, either in space, time, or space-time to accelerate a boundary integral or finite element solver pertinent to the analysis of electromagnetic radiation, scattering, or guidance problems beyond what is possible using vanilla fastmultipole methods.
Author: Albert Ruehli Publisher: John Wiley & Sons ISBN: 1118436644 Category : Technology & Engineering Languages : en Pages : 461
Book Description
Bridges the gap between electromagnetics and circuits by addressing electrometric modeling (EM) using the Partial Element Equivalent Circuit (PEEC) method This book provides intuitive solutions to electromagnetic problems by using the Partial Element Equivalent Circuit (PEEC) method. This book begins with an introduction to circuit analysis techniques, laws, and frequency and time domain analyses. The authors also treat Maxwell's equations, capacitance computations, and inductance computations through the lens of the PEEC method. Next, readers learn to build PEEC models in various forms: equivalent circuit models, non-orthogonal PEEC models, skin-effect models, PEEC models for dielectrics, incident and radiate field models, and scattering PEEC models. The book concludes by considering issues like stability and passivity, and includes five appendices some with formulas for partial elements. Leads readers to the solution of a multitude of practical problems in the areas of signal and power integrity and electromagnetic interference Contains fundamentals, applications, and examples of the PEEC method Includes detailed mathematical derivations Circuit Oriented Electromagnetic Modeling Using the PEEC Techniques is a reference for students, researchers, and developers who work on the physical layer modeling of IC interconnects and Packaging, PCBs, and high speed links.
Author: Peter Russer Publisher: Springer Science & Business Media ISBN: 3540687688 Category : Technology & Engineering Languages : en Pages : 423
Book Description
This book consists of contributions given in honor of Wolfgang J.R. Hoefer. Space and time discretizing time domain methods for electromagnetic full-wave simulation have emerged as key numerical methods in computational electromagnetics. Time domain methods are versatile and can be applied to the solution of a wide range of electromagnetic field problems. Computing the response of an electromagnetic structure to an impulsive excitation localized in space and time provides a comprehensive characterization of the electromagnetic properties of the structure in a wide frequency range. The most important methods are the Finite Difference Time Domain (FDTD) and the Transmission Line Matrix (TLM) methods. The contributions represent the state of the art in dealing with time domain methods in modern engineering electrodynamics for electromagnetic modeling in general, the Transmission Line Matrix (TLM) method, the application of network concepts to electromagnetic field modeling, circuit and system applications and, finally, with broadband devices, systems and measurement techniques.
Author: Thomas Wriedt Publisher: Springer ISBN: 3319748904 Category : Science Languages : en Pages : 258
Book Description
This book presents the Generalized Multipole Technique as a fast and powerful theoretical and computation tool to simulate light scattering by nonspherical particles. It also demonstrates the considerable potential of the method. In recent years, the concept has been applied in new fields, such as simulation of electron energy loss spectroscopy and has been used to extend other methods, like the null-field method, making it more widely applicable. The authors discuss particular implementations of the GMT methods, such as the Discrete Sources Method (DSM), Multiple Multipole Program (MMP), the Method of Auxiliary Sources (MAS), the Filamentary Current Method (FCM), the Method of Fictitious Sources (MFS) and the Null-Field Method with Discrete Sources (NFM-DS). The Generalized Multipole Technique is a surface-based method to find the solution of a boundary-value problem for a given differential equation by expanding the fields in terms of fundamental or other singular solutions of this equation. The amplitudes of these fundamental solutions are determined from the boundary condition at the particle surface. Electromagnetic and light scattering by particles or systems of particles has been the subject of intense research in various scientific and engineering fields, including astronomy, optics, meteorology, remote sensing, optical particle sizing and electromagnetics, which has led to the development of a large number of modelling methods based on the Generalized Multipole Technique for quantitative evaluation of electromagnetic scattering by particles of various shapes and compositions. The book describes these methods in detail.
Author: Vladimir Rohklin
Author: Vladimir Rohklin
Author: Jian-Ming Jin
Author: Raj Mittra
Author: Nail A Gumerov
Author: Wenhua Yu
Author: Leopold B. Felsen
Author: 
Author: Albert Ruehli
Author: Peter Russer
Author: Thomas Wriedt