Green S Functions And Finite Elements
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Green S Functions And Finite Elements
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Author : Friedel Hartmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-01
Green S Functions And Finite Elements written by Friedel Hartmann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-01 with Science categories.
This book elucidates how Finite Element methods look like from the perspective of Green’s functions, and shows new insights into the mathematical theory of Finite Elements. Practically, this new view on Finite Elements enables the reader to better assess solutions of standard programs and to find better model of a given problem. The book systematically introduces the basic concepts how Finite Elements fulfill the strategy of Green’s functions and how approximating of Green’s functions. It discusses in detail the discretization error and shows that are coherent with the strategy of “goal oriented refinement”. The book also gives much attention to the dependencies of FE solutions from the parameter set of the model.
Green S Functions And Boundary Element Analysis For Modeling Of Mechanical Behavior Of Advanced Materials
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Author : J. R. Berger
language : en
Publisher: DIANE Publishing
Release Date : 1998-03
Green S Functions And Boundary Element Analysis For Modeling Of Mechanical Behavior Of Advanced Materials written by J. R. Berger and has been published by DIANE Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-03 with Mathematics categories.
Demonstrates the potential of Green's functions & boundary element methods in solving a broad range of practical materials science problems. Papers include: Accurate Discretization of Integral Operators, Boundary Element Analysis of Bimaterials Using Anisotropic Elastic Green's Functions, Mechanical Properties of Metal-Matrix Composites, Approximate Operators for Boundary Integral Equations in Transient Elastodynamics, Simulation of the Electrochemical Machining Process Using a 2D Fundamental Singular Solution, Elastic Green's Functions for Anisotropic Solids, & more. Charts & tables.
Green S Function Integral Equation Methods In Nano Optics
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Author : Thomas M. Søndergaard
language : en
Publisher: CRC Press
Release Date : 2019-01-30
Green S Function Integral Equation Methods In Nano Optics written by Thomas M. Søndergaard and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-30 with Technology & Engineering categories.
This book gives a comprehensive introduction to Green’s function integral equation methods (GFIEMs) for scattering problems in the field of nano-optics. First, a brief review is given of the most important theoretical foundations from electromagnetics, optics, and scattering theory, including theory of waveguides, Fresnel reflection, and scattering, extinction, and absorption cross sections. This is followed by a presentation of different types of GFIEMs of increasing complexity for one-, two-, and three-dimensional scattering problems. In GFIEMs, the electromagnetic field at any position is directly related to the field at either the inside or the surface of a scattering object placed in a reference structure. The properties of the reference structure, and radiating or periodic boundary conditions, are automatically taken care of via the choice of Green’s function. This book discusses in detail how to solve the integral equations using either simple or higher-order finite-element-based methods; how to calculate the relevant Green’s function for different reference structures and choices of boundary conditions; and how to calculate near-fields, optical cross sections, and the power emitted by a local source. Solution strategies for large structures are discussed based on either transfer-matrix-approaches or the conjugate gradient algorithm combined with the Fast Fourier Transform. Special attention is given to reducing the computational problem for three-dimensional structures with cylindrical symmetry by using cylindrical harmonic expansions. Each presented method is accompanied by examples from nano-optics, including: resonant metal nano-particles placed in a homogeneous medium or on a surface or waveguide; a microstructured gradient-index-lens; the Purcell effect for an emitter in a photonic crystal; the excitation of surface plasmon polaritons by second-harmonic generation in a polymer fiber placed on a thin metal film; and anti-reflective, broadband absorbing or resonant surface microstructures. Each presented method is also accompanied by guidelines for software implementation and exercises. Features Comprehensive introduction to Green’s function integral equation methods for scattering problems in the field of nano-optics Detailed explanation of how to discretize and solve integral equations using simple and higher-order finite-element approaches Solution strategies for large structures Guidelines for software implementation and exercises Broad selection of examples of scattering problems in nano-optics
Statics And Influence Functions
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Author : Friedel Hartmann
language : en
Publisher: Springer Nature
Release Date : 2020-11-25
Statics And Influence Functions written by Friedel Hartmann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-25 with Science categories.
This extended and revised second edition is intended for engineering students and researchers working with finite element methods in structural and mechanical analysis. Discussing numerical structural analysis from first mechanical and mathematical principles, it establishes the central role of influence functions (Green's functions) in finite element analysis, reanalysis, sensitivity analysis, parameter identification and in optimization, with a particular focus on computational aspects and questions of accuracy. It also presents a one-click reanalysis, a new technique that allows instantaneous modifications to a structure to be made by clicking on single elements. Lastly, the book features four programs that can be downloaded for the solution of the Poisson equation, 2-D elasticity, plate-bending problems and planar frames.
Numerical Solution Of Partial Differential Equations By The Finite Element Method
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Author : Claes Johnson
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23
Numerical Solution Of Partial Differential Equations By The Finite Element Method written by Claes Johnson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Mathematics categories.
An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.
Green S Function Finite Elements And Microwave Planar Circuits
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Author : J. Helszajn
language : en
Publisher:
Release Date : 1996-11-29
Green S Function Finite Elements And Microwave Planar Circuits written by J. Helszajn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-11-29 with Mathematics categories.
The application of Green?s function to planar microwave circuits is now very well accepted as a fundamental tool in electromagnetic analysis. Combining various modern mathematical techniques this book presents comprehensive and detailed methods for numerically describing practical microwave circuits (with one or more ports). Features include: Applications of Green?s function in: planar resonators, gyromagnetic circuits and junction circulators, together with applied examples Detailed explanation of the use of Finite Element Method (FEM) techniques for calculating the solution of planar isotropic and gyromagnetic circuits Specifically written for industrial engineers specialising in the analysis and development of planar circuits and postgraduate researchers A perfect companion text for developing software for the solution of microwave circuits.
Green S Function And Boundary Elements Of Multifield Materials
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Author : Qing-Hua Qin
language : en
Publisher: Elsevier
Release Date : 2010-07-07
Green S Function And Boundary Elements Of Multifield Materials written by Qing-Hua Qin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-07 with Technology & Engineering categories.
Green's Function and Boundary Elements of Multifield Materials contains a comprehensive treatment of multifield materials under coupled thermal, magnetic, electric, and mechanical loads. Its easy-to-understand text clarifies some of the most advanced techniques for deriving Green's function and the related boundary element formulation of magnetoelectroelastic materials: Radon transform, potential function approach, Fourier transform. Our hope in preparing this book is to attract interested readers and researchers to a new field that continues to provide fascinating and technologically important challenges. You will benefit from the authors' thorough coverage of general principles for each topic, followed by detailed mathematical derivation and worked examples as well as tables and figures where appropriate. - In-depth explanations of the concept of Green's function - Coupled thermo-magneto-electro-elastic analysis - Detailed mathematical derivation for Green's functions
Journal Of Research Of The National Bureau Of Standards
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Author : United States. National Bureau of Standards
language : en
Publisher:
Release Date : 1987
Journal Of Research Of The National Bureau Of Standards written by United States. National Bureau of Standards and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Chemistry categories.
Green S Functions With Applications
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Author : Dean G. Duffy
language : en
Publisher: CRC Press
Release Date : 2015-03-10
Green S Functions With Applications written by Dean G. Duffy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-10 with Mathematics categories.
Since publication of the first edition over a decade ago, Green’s Functions with Applications has provided applied scientists and engineers with a systematic approach to the various methods available for deriving a Green’s function. This fully revised Second Edition retains the same purpose, but has been meticulously updated to reflect the current state of the art. The book opens with necessary background information: a new chapter on the historical development of the Green’s function, coverage of the Fourier and Laplace transforms, a discussion of the classical special functions of Bessel functions and Legendre polynomials, and a review of the Dirac delta function. The text then presents Green’s functions for each class of differential equation (ordinary differential, wave, heat, and Helmholtz equations) according to the number of spatial dimensions and the geometry of the domain. Detailing step-by-step methods for finding and computing Green’s functions, each chapter contains a special section devoted to topics where Green’s functions particularly are useful. For example, in the case of the wave equation, Green’s functions are beneficial in describing diffraction and waves. To aid readers in developing practical skills for finding Green’s functions, worked examples, problem sets, and illustrations from acoustics, applied mechanics, antennas, and the stability of fluids and plasmas are featured throughout the text. A new chapter on numerical methods closes the book. Included solutions and hundreds of references to the literature on the construction and use of Green's functions make Green’s Functions with Applications, Second Edition a valuable sourcebook for practitioners as well as graduate students in the sciences and engineering.
Automated Solution Of Differential Equations By The Finite Element Method
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Author : Anders Logg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-24
Automated Solution Of Differential Equations By The Finite Element Method written by Anders Logg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-24 with Computers categories.
This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.