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| Author | : Özgür Salih Ergül |
| Publisher | : |
| Total Pages | : 328 |
| Release | : 2003 |
| Genre | : Electromagnetic theory |
| ISBN | : |
| Author | : Caleb Waltz |
| Publisher | : |
| Total Pages | : 186 |
| Release | : 2005 |
| Genre | : Moment problems (Mathematics) |
| ISBN | : |
Abstract: In this thesis, we propose a massively parallelizable version of the single level fast multipole method that outperforms the conventional algorithm for large problems. We show that this version of the algorithm has a lower 0(N6/5) complexity (N denotes the matrix size) as compared to the conventional single level fast multipole method, which scales as O(N3/2). We demonstrate that the multilevel fast multipole algorithm (ML-FMA) performs poorly in a parallel setting when dealing with electrically large geometries, due to its overwhelming communication bottleneck among processors. Through numerical examples we demonstrate that the proposed parallel fast multipole method yields smaller memory and time requirements than its multilevel counterpart.
| Author | : Ralf Theo Jacobs |
| Publisher | : |
| Total Pages | : 144 |
| Release | : 2009 |
| Genre | : |
| ISBN | : 9783941298323 |
| Author | : Nail A Gumerov |
| Publisher | : Elsevier |
| Total Pages | : 551 |
| Release | : 2005-01-27 |
| Genre | : Mathematics |
| ISBN | : 0080531598 |
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 | : Walton C. Gibson |
| Publisher | : CRC Press |
| Total Pages | : 510 |
| Release | : 2021-09-06 |
| Genre | : Mathematics |
| ISBN | : 1000412482 |
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.
| Author | : Thomas Wriedt |
| Publisher | : Springer |
| Total Pages | : 258 |
| Release | : 2018-03-09 |
| Genre | : Science |
| ISBN | : 3319748904 |
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 | : Ozgur Ergul |
| Publisher | : John Wiley & Sons |
| Total Pages | : 484 |
| Release | : 2014-04-22 |
| Genre | : Science |
| ISBN | : 1118844912 |
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.
| Author | : Y. Zhang |
| Publisher | : John Wiley & Sons |
| Total Pages | : 367 |
| Release | : 2009-06-29 |
| Genre | : Science |
| ISBN | : 0470495081 |
A step-by-step guide to parallelizing cem codes The future of computational electromagnetics is changing drastically as the new generation of computer chips evolves from single-core to multi-core. The burden now falls on software programmers to revamp existing codes and add new functionality to enable computational codes to run efficiently on this new generation of multi-core CPUs. In this book, you'll learn everything you need to know to deal with multi-core advances in chip design by employing highly efficient parallel electromagnetic code. Focusing only on the Method of Moments (MoM), the book covers: In-Core and Out-of-Core LU Factorization for Solving a Matrix Equation A Parallel MoM Code Using RWG Basis Functions and ScaLAPACK-Based In-Core and Out-of-Core Solvers A Parallel MoM Code Using Higher-Order Basis Functions and ScaLAPACK-Based In-Core and Out-of-Core Solvers Turning the Performance of a Parallel Integral Equation Solver Refinement of the Solution Using the Conjugate Gradient Method A Parallel MoM Code Using Higher-Order Basis Functions and Plapack-Based In-Core and Out-of-Core Solvers Applications of the Parallel Frequency Domain Integral Equation Solver Appendices are provided with detailed information on the various computer platforms used for computation; a demo shows you how to compile ScaLAPACK and PLAPACK on the Windows® operating system; and a demo parallel source code is available to solve the 2D electromagnetic scattering problems. Parallel Solution of Integral Equation-Based EM Problems in the Frequency Domain is indispensable reading for computational code designers, computational electromagnetics researchers, graduate students, and anyone working with CEM software.
| Author | : |
| Publisher | : |
| Total Pages | : 19 |
| Release | : 2005 |
| Genre | : |
| ISBN | : |
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 | : Si Chuen Michael Yeung |
| Publisher | : |
| Total Pages | : 454 |
| Release | : 1995 |
| Genre | : |
| ISBN | : |
