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Author: Shaojing Li
Publisher:
ISBN: 9781267685155
Category :
Languages : en
Pages : 217
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Book Description
In this thesis, fast algorithms for solving fields defined by the Helmholtz equation using integral equation methods are developed and implemented on Graphics Processing Units (GPUs). GPUs are massively parallel processors that offer tens or even hundreds of times of floating point computing capability to current generation CPUs. A short history of the GPUs is given and their unique architecture is described in details. On this new hardware architecture, algorithms like the hierarchical Non-uniform Grid Interpolation Method (NGIM) and the FFT-based Adaptive Integral Method (AIM) have to be significant changed from their original sequential forms to achieve high performances. Specifically, the computational domains of the problems are divided into boxes, homoge-nizing the computing burdens across the wide SIMD-style stream multiprocessors. Computing operations are reformed and reorganized to exploit the enormous floating point computing power and while at the same time to minimize the data transfer latencies. The achieved computing performance on commercial GPUs is generally two orders of magnitude higher than that on state-of-the-art CPUs and with much lower memory consumption. Based on these fast algorithms, an ultra-fast micromagnetic solver with linear or computational complexity is built. This solver, named FastMag, runs on desktop workstations with one or several GPU cards and is able to simulate magnetic systems with over one hundred million degrees of freedom. Electromagnetic solvers that use slightly different algorithms are also implemented and provide impressive performance on general electromagnetic problems such as wave scattering. This electromagnetic solver is also capable of handling periodic boundary problems using a new algorithm called the Fast Periodic Interpolation Method (FPIM). This algorithm significantly uses spatial interpolations as well as the FFT to reduce the time of evaluating fields generated by infinitely periodic structures. Using previously developed micromagnetic solvers, the author investigated two novel magnetic recording systems that might be useful in the next generation ultra-high density magnetic recording. The capped bit-patterned media (CBPM) are proposed to have lower reversal fields, lower switching field distribution as well as better readback signals. The reversal mechanisms of bit-patterned media under the influence of microwaves are also investigated. This leads to the proposed multi-layer recording system using the microwave-assisted magnetic recording (MAMR) technology.
Author: Shaojing Li
Publisher:
ISBN: 9781267685155
Category :
Languages : en
Pages : 217
Get Book Here
Book Description
In this thesis, fast algorithms for solving fields defined by the Helmholtz equation using integral equation methods are developed and implemented on Graphics Processing Units (GPUs). GPUs are massively parallel processors that offer tens or even hundreds of times of floating point computing capability to current generation CPUs. A short history of the GPUs is given and their unique architecture is described in details. On this new hardware architecture, algorithms like the hierarchical Non-uniform Grid Interpolation Method (NGIM) and the FFT-based Adaptive Integral Method (AIM) have to be significant changed from their original sequential forms to achieve high performances. Specifically, the computational domains of the problems are divided into boxes, homoge-nizing the computing burdens across the wide SIMD-style stream multiprocessors. Computing operations are reformed and reorganized to exploit the enormous floating point computing power and while at the same time to minimize the data transfer latencies. The achieved computing performance on commercial GPUs is generally two orders of magnitude higher than that on state-of-the-art CPUs and with much lower memory consumption. Based on these fast algorithms, an ultra-fast micromagnetic solver with linear or computational complexity is built. This solver, named FastMag, runs on desktop workstations with one or several GPU cards and is able to simulate magnetic systems with over one hundred million degrees of freedom. Electromagnetic solvers that use slightly different algorithms are also implemented and provide impressive performance on general electromagnetic problems such as wave scattering. This electromagnetic solver is also capable of handling periodic boundary problems using a new algorithm called the Fast Periodic Interpolation Method (FPIM). This algorithm significantly uses spatial interpolations as well as the FFT to reduce the time of evaluating fields generated by infinitely periodic structures. Using previously developed micromagnetic solvers, the author investigated two novel magnetic recording systems that might be useful in the next generation ultra-high density magnetic recording. The capped bit-patterned media (CBPM) are proposed to have lower reversal fields, lower switching field distribution as well as better readback signals. The reversal mechanisms of bit-patterned media under the influence of microwaves are also investigated. This leads to the proposed multi-layer recording system using the microwave-assisted magnetic recording (MAMR) technology.
Author: Sidi Fu
Publisher:
ISBN:
Category :
Languages : en
Pages : 159
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Book Description
Micromagnetics is a field of study considering the magnetization behavior in magnetic materials and devices accounting for a wide set of interactions and describing the magnetization phenomena from the atomistic scale to several hundreds of microns. Micromagnetic simulations are essential in understanding the behavior of many magnetic systems. Modeling complex structures can require a significant computational time and in some cases, the system complexity can make simulations prohibitively long or require a prohibitively large memory. In this thesis, we present a set of methods and their implementations that resulted in high-performance numerical micromagnetic tools for modeling highly complex magnetic materials and devices. The focus of the dissertation is on solving Landau-Lifshitz-Gilbert (LLG) equation efficiently, both with numerical methods and advanced hardware acceleration. To understand the numerical problem to be solved, the introduction Chapter 1 addresses the LLG equation and the governing interactions involved as well as numerical modeling basics on the Finite Difference Method (FDM) and the Finite Element Method (FEM). Chapter 1 also presents a versatile micromagnetic framework, referred to as FastMag, which implements some of these methods. Chapter 2 provides a detailed description of computing based on Graphics Processing Units (GPUs). The history of GPU programming model and the programming tips serve as the basis for understanding parallel computing on GPUs. It presents applications of GPUs on various platforms to demonstrate the current mainstream usage of GPUs and their promising future development direction. Chapter 2 also summarizes applications of GPUs in micromagnetics. Chapters 3 and 4 address two essential aspects of micromagnetic solvers: fast algorithms for computing the key interaction components and efficient time integration methods. Chapter 3 introduces a non-uniform Fourier transform (NUFFT) method, a scalar potential method, and sparse matrix-vector multiplication (SpMVM) algorithms implemented on GPUs to accelerate the magnetostatic and exchange interactions. Chapter 4 addresses basics of the time integration methods used in FastMag as well as a preconditioner to further accelerate the time integration process. Chapter 5 presents a numerical model for the current state-of-art magnetic recording system using advanced algorithms and GPU implementations described in Chapters 2-4.
Author: Wen-mei Hwu
Publisher: Elsevier
ISBN: 0123859638
Category : Computers
Languages : en
Pages : 562
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Book Description
"Since the introduction of CUDA in 2007, more than 100 million computers with CUDA capable GPUs have been shipped to end users. GPU computing application developers can now expect their application to have a mass market. With the introduction of OpenCL in 2010, researchers can now expect to develop GPU applications that can run on hardware from multiple vendors"--
Author: Walton C. Gibson
Publisher: CRC Press
ISBN: 1000412482
Category : Mathematics
Languages : en
Pages : 510
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Book Description
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: Sidney Yip
Publisher: Springer Science & Business Media
ISBN: 1402032862
Category : Science
Languages : en
Pages : 2903
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Book Description
The first reference of its kind in the rapidly emerging field of computational approachs to materials research, this is a compendium of perspective-providing and topical articles written to inform students and non-specialists of the current status and capabilities of modelling and simulation. From the standpoint of methodology, the development follows a multiscale approach with emphasis on electronic-structure, atomistic, and mesoscale methods, as well as mathematical analysis and rate processes. Basic models are treated across traditional disciplines, not only in the discussion of methods but also in chapters on crystal defects, microstructure, fluids, polymers and soft matter. Written by authors who are actively participating in the current development, this collection of 150 articles has the breadth and depth to be a major contributor toward defining the field of computational materials. In addition, there are 40 commentaries by highly respected researchers, presenting various views that should interest the future generations of the community. Subject Editors: Martin Bazant, MIT; Bruce Boghosian, Tufts University; Richard Catlow, Royal Institution; Long-Qing Chen, Pennsylvania State University; William Curtin, Brown University; Tomas Diaz de la Rubia, Lawrence Livermore National Laboratory; Nicolas Hadjiconstantinou, MIT; Mark F. Horstemeyer, Mississippi State University; Efthimios Kaxiras, Harvard University; L. Mahadevan, Harvard University; Dimitrios Maroudas, University of Massachusetts; Nicola Marzari, MIT; Horia Metiu, University of California Santa Barbara; Gregory C. Rutledge, MIT; David J. Srolovitz, Princeton University; Bernhardt L. Trout, MIT; Dieter Wolf, Argonne National Laboratory.
Author: Wolfgang Hackbusch
Publisher: Springer
ISBN: 3662473240
Category : Mathematics
Languages : en
Pages : 532
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Book Description
This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.
Author: Dietrich Braess
Publisher: Cambridge University Press
ISBN: 113946146X
Category : Mathematics
Languages : en
Pages : 348
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Book Description
This definitive introduction to finite element methods was thoroughly updated for this 2007 third edition, which features important material for both research and application of the finite element method. The discussion of saddle-point problems is a highlight of the book and has been elaborated to include many more nonstandard applications. The chapter on applications in elasticity now contains a complete discussion of locking phenomena. The numerical solution of elliptic partial differential equations is an important application of finite elements and the author discusses this subject comprehensively. These equations are treated as variational problems for which the Sobolev spaces are the right framework. Graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite element methods will find this text invaluable. Specifically, the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering.
Author: Victorino Franco
Publisher: Springer Nature
ISBN: 3030704432
Category : Technology & Engineering
Languages : en
Pages : 814
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Book Description
This book discusses the most commonly used techniques for characterizing magnetic material properties and their applications. It provides a comprehensive and easily digestible collection and review of magnetic measurement techniques. It also examines the underlying operating principles and techniques of magnetic measurements, and presents current examples where such measurements and properties are relevant. Given the pervasive nature of magnetic materials in everyday life, this book is a vital resource for both professionals and students wishing to deepen their understanding of the subject.
Author: Bruce Berne
Publisher: Springer
ISBN: 9781468425550
Category : Science
Languages : en
Pages : 242
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Book Description
The last decade has been marked by a rapid growth in statistical mechanics, especially in connection with the physics and chemistry of the fluid state. Our understanding in these areas has been considerably advanced and enriched by the discovery of new techniques and the sharpening of old techniques, ranging all the way from computer simulation to mode-mode coupling theories. Statistical mechanics brings together under one roof a broad spectrum of mathematical techniques. The aim of these volumes is to provide a didactic treatment of those techniques that are most useful for the study of problems of current interest to theoretical chemists. The emphasis throughout is on the techniques themselves and not on reviewing the enormous literature in statistical mechanics. Each author was charged with the following task. Given N pages, (a) pose the problem, (b) present those aspects of the particular technique that clearly illustrate its internal workings, (c) apply the technique to the solution of several illustrative examples, and (d) write the chapter so that it will enable the reader to approach key citations to the literature intelligently. These volumes are designed for graduate students and research workers in statistical mechanics. Nevertheless, because of the range of techniques and their general utility, they should be useful in other areas as well.
Author: Hari Singh Nalwa
Publisher:
ISBN: 9781588830005
Category : Science
Languages : en
Pages : 0
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Book Description
Twelve contributions comprise a reference source that is a coherent presentation of the state of the art in this fast growing area of nanotechnology research. Magnetic nanostructures are important for their phenomenal potential for storage; their great commercial value will come from applications in
