Generalized Collocation Methods

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Generalized Collocation Methods

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Author : Nicola Bellomo
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-16

Generalized Collocation Methods written by Nicola Bellomo 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 2007-10-16 with Mathematics categories.

Analysis of nonlinear models and problems is crucial in the application of mathematics to real-world problems. This book approaches this important topic by focusing on collocation methods for solving nonlinear evolution equations and applying them to a variety of mathematical problems. These include wave motion models, hydrodynamic models of vehicular traffic flow, convection-diffusion models, reaction-diffusion models, and population dynamics models. The book may be used as a textbook for graduate courses on collocation methods, nonlinear modeling, and nonlinear differential equations. Examples and exercises are included in every chapter.

Generalized Multipole Techniques For Electromagnetic And Light Scattering

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Author : T. Wriedt
language : en
Publisher: Elsevier
Release Date : 1999-12-01

Generalized Multipole Techniques For Electromagnetic And Light Scattering written by T. Wriedt and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-01 with Technology & Engineering categories.

This book is an edited volume of nine papers covering the different variants of the generalized multipole techniques (GMT). The papers were presented at the recent 3rd Workshop on Electromagnetics and Light Scattering - Theory and Applications, which focused on current GMT methods. These include the multiple multipole method (MMP), the discrete sources method (DSM), Yasuura's method, method of auxiliary sources and null-field method with discrete sources. Each paper presents a full theoretical description as well as some applications of the method in electrical engineering and optics. It also includes both 2D and 3D methods and other applications developed in the former Soviet Union and Japan.

Spectral And High Order Methods For Partial Differential Equations

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Author : Jan S. Hesthaven
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-29

Spectral And High Order Methods For Partial Differential Equations written by Jan S. Hesthaven 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 2010-10-29 with Mathematics categories.

The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2009), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography.

American Environmentalism

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Author : J. Michael Martinez
language : en
Publisher: CRC Press
Release Date : 2013-06-20

American Environmentalism written by J. Michael Martinez and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-20 with Law categories.

Protecting the natural environment and promoting sustainability have become important objectives, but achieving such goals presents myriad challenges for even the most committed environmentalist. American Environmentalism: Philosophy, History, and Public Policy examines whether competing interests can be reconciled while developing consistent, coherent, effective public policy to regulate uses and protection of the natural environment without destroying the national economy. It then reviews a range of possible solutions. The book delves into key normative concepts that undergird American perspectives on nature by providing an overview of philosophical concepts found in the western intellectual tradition, the presuppositions inherent in neoclassical economics, and anthropocentric (human-centered) and biocentric (earth-centered) positions on sustainability. It traces the evolution of attitudes about nature from the time of the Ancient Greeks through Europeans in the Middle Ages and the Renaissance, the Enlightenment and the American Founders, the nineteenth and twentieth centuries, and up to the present. Building on this foundation, the author examines the political landscape as non-governmental organizations (NGOs), industry leaders, and government officials struggle to balance industrial development with environmental concerns. Outrageous claims, silly misrepresentations, bogus arguments, absurd contentions, and overblown prophesies of impending calamities are bandied about by many parties on all sides of the debate—industry spokespeople, elected representatives, unelected regulators, concerned citizens, and environmental NGOs alike. In lieu of descending into this morass, the author circumvents the silliness to explore the crucial issues through a more focused, disciplined approach. Rather than engage in acrimonious debate over minutiae, as so often occurs in the context of "green" claims, he recasts the issue in a way that provides a cohesive look at all sides. This effort may be quixotic, but how else to cut the Gordian knot?

Generalized Differential And Integral Quadrature

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Author : Francesco Tornabene
language : en
Publisher: Società Editrice Esculapio
Release Date : 2023-10-17

Generalized Differential And Integral Quadrature written by Francesco Tornabene and has been published by Società Editrice Esculapio this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-17 with Technology & Engineering categories.

The main aim of this book is to analyze the mathematical fundamentals and the main features of the Generalized Differential Quadrature (GDQ) and Generalized Integral Quadrature (GIQ) techniques. Furthermore, another interesting aim of the present book is to shown that from the two numerical techniques mentioned above it is possible to derive two different approaches such as the Strong and Weak Finite Element Methods (SFEM and WFEM), that will be used to solve various structural problems and arbitrarily shaped structures. A general approach to the Differential Quadrature is proposed. The weighting coefficients for different basis functions and grid distributions are determined. Furthermore, the expressions of the principal approximating polynomials and grid distributions, available in the literature, are shown. Besides the classic orthogonal polynomials, a new class of basis functions, which depend on the radial distance between the discretization points, is presented. They are known as Radial Basis Functions (or RBFs). The general expressions for the derivative evaluation can be utilized in the local form to reduce the computational cost. From this concept the Local Generalized Differential Quadrature (LGDQ) method is derived. The Generalized Integral Quadrature (GIQ) technique can be used employing several basis functions, without any restriction on the point distributions for the given definition domain. To better underline these concepts some classical numerical integration schemes are reported, such as the trapezoidal rule or the Simpson method. An alternative approach based on Taylor series is also illustrated to approximate integrals. This technique is named as Generalized Taylor-based Integral Quadrature (GTIQ) method. The major structural theories for the analysis of the mechanical behavior of various structures are presented in depth in the book. In particular, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. Generally speaking, two formulations of the same system of governing equations can be developed, which are respectively the strong and weak (or variational) formulations. Once the governing equations that rule a generic structural problem are obtained, together with the corresponding boundary conditions, a differential system is written. In particular, the Strong Formulation (SF) of the governing equations is obtained. The differentiability requirement, instead, is reduced through a weighted integral statement if the corresponding Weak Formulation (WF) of the governing equations is developed. Thus, an equivalent integral formulation is derived, starting directly from the previous one. In particular, the formulation in hand is obtained by introducing a Lagrangian approximation of the degrees of freedom of the problem. The need of studying arbitrarily shaped domains or characterized by mechanical and geometrical discontinuities leads to the development of new numerical approaches that divide the structure in finite elements. Then, the strong form or the weak form of the fundamental equations are solved inside each element. The fundamental aspects of this technique, which the author defined respectively Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM), are presented in the book.

Wavelet Methods For Solving Partial Differential Equations And Fractional Differential Equations

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Author : Santanu Saha Ray
language : en
Publisher: CRC Press
Release Date : 2018-01-12

Wavelet Methods For Solving Partial Differential Equations And Fractional Differential Equations written by Santanu Saha Ray and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-12 with Mathematics categories.

The main focus of the book is to implement wavelet based transform methods for solving problems of fractional order partial differential equations arising in modelling real physical phenomena. It explores analytical and numerical approximate solution obtained by wavelet methods for both classical and fractional order partial differential equations.

Multidisciplinary Approach In Research Area Volume 7

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Author : Chief Editor- Biplab Auddya, Editor- Dr. Tarannum Khan, Bijanamula Supriya, Dr. Jyotsana Khandelwal, Mrs. V.Geetha, Smt. Padmini Kaji, Mercy Varshney
language : en
Publisher: The Hill Publication
Release Date : 2024-03-14

Multidisciplinary Approach In Research Area Volume 7 written by Chief Editor- Biplab Auddya, Editor- Dr. Tarannum Khan, Bijanamula Supriya, Dr. Jyotsana Khandelwal, Mrs. V.Geetha, Smt. Padmini Kaji, Mercy Varshney and has been published by The Hill Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-14 with Antiques & Collectibles categories.

Differential Quadrature And Its Application In Engineering

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Author : Chang Shu
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-01-14

Differential Quadrature And Its Application In Engineering written by Chang Shu 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 2000-01-14 with Mathematics categories.

In the past few years, the differential quadrature method has been applied extensively in engineering. This book, aimed primarily at practising engineers, scientists and graduate students, gives a systematic description of the mathematical fundamentals of differential quadrature and its detailed implementation in solving Helmholtz problems and problems of flow, structure and vibration. Differential quadrature provides a global approach to numerical discretization, which approximates the derivatives by a linear weighted sum of all the functional values in the whole domain. Following the analysis of function approximation and the analysis of a linear vector space, it is shown in the book that the weighting coefficients of the polynomial-based, Fourier expansion-based, and exponential-based differential quadrature methods can be computed explicitly. It is also demonstrated that the polynomial-based differential quadrature method is equivalent to the highest-order finite difference scheme. Furthermore, the relationship between differential quadrature and conventional spectral collocation is analysed. The book contains material on: - Linear Vector Space Analysis and the Approximation of a Function; - Polynomial-, Fourier Expansion- and Exponential-based Differential Quadrature; - Differential Quadrature Weighting Coefficient Matrices; - Solution of Differential Quadrature-resultant Equations; - The Solution of Incompressible Navier-Stokes and Helmholtz Equations; - Structural and Vibrational Analysis Applications; - Generalized Integral Quadrature and its Application in the Solution of Boundary Layer Equations. Three FORTRAN programs for simulation of driven cavity flow, vibration analysis of plate and Helmholtz eigenvalue problems respectively, are appended. These sample programs should give the reader a better understanding of differential quadrature and can easily be modified to solve the readers own engineering problems.

Advanced Methods For Geometric Modeling And Numerical Simulation

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Author : Carlotta Giannelli
language : en
Publisher: Springer Nature
Release Date : 2019-09-18

Advanced Methods For Geometric Modeling And Numerical Simulation written by Carlotta Giannelli and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-18 with Mathematics categories.

This book gathers selected contributions presented at the INdAM Workshop “DREAMS”, held in Rome, Italy on January 22−26, 2018. Addressing cutting-edge research topics and advances in computer aided geometric design and isogeometric analysis, it covers distinguishing curve/surface constructions and spline models, with a special focus on emerging adaptive spline constructions, fundamental spline theory and related algorithms, as well as various aspects of isogeometric methods, e.g. efficient quadrature rules and spectral analysis for isogeometric B-spline discretizations. Applications in finite element and boundary element methods are also discussed. Given its scope, the book will be of interest to both researchers and graduate students working in these areas.

Numerical Methods For Stochastic Computations

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Author : Dongbin Xiu
language : en
Publisher: Princeton University Press
Release Date : 2010-07-01

Numerical Methods For Stochastic Computations written by Dongbin Xiu and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-01 with Mathematics categories.

The@ first graduate-level textbook to focus on fundamental aspects of numerical methods for stochastic computations, this book describes the class of numerical methods based on generalized polynomial chaos (gPC). These fast, efficient, and accurate methods are an extension of the classical spectral methods of high-dimensional random spaces. Designed to simulate complex systems subject to random inputs, these methods are widely used in many areas of computer science and engineering. The book introduces polynomial approximation theory and probability theory; describes the basic theory of gPC methods through numerical examples and rigorous development; details the procedure for converting stochastic equations into deterministic ones; using both the Galerkin and collocation approaches; and discusses the distinct differences and challenges arising from high-dimensional problems. The last section is devoted to the application of gPC methods to critical areas such as inverse problems and data assimilation. Ideal for use by graduate students and researchers both in the classroom and for self-study, Numerical Methods for Stochastic Computations provides the required tools for in-depth research related to stochastic computations. The first graduate-level textbook to focus on the fundamentals of numerical methods for stochastic computations Ideal introduction for graduate courses or self-study Fast, efficient, and accurate numerical methods Polynomial approximation theory and probability theory included Basic gPC methods illustrated through examples