Meshfree Approximation Methods With Matlab
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Meshfree Approximation Methods With Matlab
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Author : Gregory E. Fasshauer
language : en
Publisher: World Scientific
Release Date : 2007
Meshfree Approximation Methods With Matlab written by Gregory E. Fasshauer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Technology & Engineering categories.
Meshfree approximation methods are a relatively new area of research. This book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. It places emphasis on a hands-on approach that includes MATLAB routines for all basic operations.
Meshfree Approximation Methods With Matlab
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Author : Gregory E. Fasshauer
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2007-01-01
Meshfree Approximation Methods With Matlab written by Gregory E. Fasshauer and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present. Whereas other works focus almost entirely on theoretical aspects or applications in the engineering field, this book provides the salient theoretical result needed for a basic understanding of meshfree approximation methods. The emphasis here is on a hands-on approach that includes Matlab routines for all basic operations. Meshfree approximation methods, such as radial basis function and moving least squares method, are discussed from a scattered data approximation and partial differential equations point of view. A good balance is supplied between the necessary theory and implementation in terms of many Matlab programs, with examples and applications to illustrate key points. Used as class notes for graduate courses at Northwestern University, Illinois Institute of Technology, and Vanderbilt University, this book will appeal to both mathematics and engineering graduate students.
Meshfree Approximation Methods With Matlab With Cd Rom
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Author : Gregory E Fasshauer
language : en
Publisher: World Scientific Publishing Company
Release Date : 2007-04-17
Meshfree Approximation Methods With Matlab With Cd Rom written by Gregory E Fasshauer and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-17 with Mathematics categories.
Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present. Whereas other works focus almost entirely on theoretical aspects or applications in the engineering field, this book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods.The emphasis here is on a hands-on approach that includes MATLAB routines for all basic operations. Meshfree approximation methods, such as radial basis function and moving least squares method, are discussed from a scattered data approximation and partial differential equations point of view. A good balance is supplied between the necessary theory and implementation in terms of many MATLAB programs, with examples and applications to illustrate key points. Used as class notes for graduate courses at Northwestern University, Illinois Institute of Technology, and Vanderbilt University, this book will appeal to both mathematics and engineering graduate students.
Kernel Based Approximation Methods Using Matlab
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Author : Gregory E Fasshauer
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-07-30
Kernel Based Approximation Methods Using Matlab written by Gregory E Fasshauer and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-30 with Mathematics categories.
In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.
An Introduction To Meshfree Methods And Their Programming
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Author : G.R. Liu
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-05
An Introduction To Meshfree Methods And Their Programming written by G.R. Liu 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 2005-12-05 with Technology & Engineering categories.
The finite difference method (FDM) hasbeen used tosolve differential equation systems for centuries. The FDM works well for problems of simple geometry and was widely used before the invention of the much more efficient, robust finite element method (FEM). FEM is now widely used in handling problems with complex geometry. Currently, we are using and developing even more powerful numerical techniques aiming to obtain more accurate approximate solutions in a more convenient manner for even more complex systems. The meshfree or meshless method is one such phenomenal development in the past decade, and is the subject of this book. There are many MFree methods proposed so far for different applications. Currently, three monographs on MFree methods have been published. Mesh Free Methods, Moving Beyond the Finite Element Method d by GR Liu (2002) provides a systematic discussion on basic theories, fundamentals for MFree methods, especially on MFree weak-form methods. It provides a comprehensive record of well-known MFree methods and the wide coverage of applications of MFree methods to problems of solids mechanics (solids, beams, plates, shells, etc.) as well as fluid mechanics. The Meshless Local Petrov-Galerkin (MLPG) Method d by Atluri and Shen (2002) provides detailed discussions of the meshfree local Petrov-Galerkin (MLPG) method and itsvariations. Formulations and applications of MLPG are well addressed in their book.
Meshfree Methods For Partial Differential Equations Iv
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Author : Michael Griebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-10
Meshfree Methods For Partial Differential Equations Iv written by Michael Griebel 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 2008-10-10 with Mathematics categories.
The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the proceedings papers of the Fourth International Workshop on Meshfree Methods held in September 2007 in Bonn. The articles address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM, etc.) and their application in applied mathematics, physics and engineering. The volume is intended to foster this very active and exciting area of interdisciplinary research and to present recent advances and results in this field.
Meshfree Methods For Partial Differential Equations Ix
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Author : Michael Griebel
language : en
Publisher: Springer
Release Date : 2019-06-19
Meshfree Methods For Partial Differential Equations Ix written by Michael Griebel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-19 with Mathematics categories.
This volume collects selected papers presented at the Ninth International Workshop on Meshfree Methods held in Bonn, Germany in September 2017. They address various aspects of this very active research field and cover topics from applied mathematics, physics and engineering. The numerical treatment of partial differential equations with meshfree discretization techniques has been a very active research area in recent years. While the fundamental theory of meshfree methods has been developed and considerable advances of the various methods have been made, many challenges in the mathematical analysis and practical implementation of meshfree methods remain. This symposium aims to promote collaboration among engineers, mathematicians, and computer scientists and industrial researchers to address the development, mathematical analysis, and application of meshfree and particle methods especially to multiscale phenomena. It continues the2-year-cycled Workshops on Meshfree Methods for Partial Differential Equations.
Mesh Methods
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Author : Viktor A. Rukavishnikov
language : en
Publisher: MDPI
Release Date : 2021-03-29
Mesh Methods written by Viktor A. Rukavishnikov and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-29 with Mathematics categories.
Mathematical models of various natural processes are described by differential equations, systems of partial differential equations and integral equations. In most cases, the exact solution to such problems cannot be determined; therefore, one has to use grid methods to calculate an approximate solution using high-performance computing systems. These methods include the finite element method, the finite difference method, the finite volume method and combined methods. In this Special Issue, we bring to your attention works on theoretical studies of grid methods for approximation, stability and convergence, as well as the results of numerical experiments confirming the effectiveness of the developed methods. Of particular interest are new methods for solving boundary value problems with singularities, the complex geometry of the domain boundary and nonlinear equations. A part of the articles is devoted to the analysis of numerical methods developed for calculating mathematical models in various fields of applied science and engineering applications. As a rule, the ideas of symmetry are present in the design schemes and make the process harmonious and efficient.
Boundary Elements And Other Mesh Reduction Methods Xli
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Author : Cheng, A. H-D.
language : en
Publisher: WIT Press
Release Date : 2019-01-30
Boundary Elements And Other Mesh Reduction Methods Xli written by Cheng, A. H-D. and has been published by WIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-30 with Mathematics categories.
Containing the proceedings from the 41st conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM), this book is a collection of high quality papers that report on advances in techniques that reduce or eliminate the type of meshes associated with such methods as finite elements or finite differences.
Spline Functions
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Author : Larry L. Schumaker
language : en
Publisher: SIAM
Release Date : 2024-12-09
Spline Functions written by Larry L. Schumaker and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-09 with Mathematics categories.
This book is a continuation of the author’s earlier book Spline Functions: Computational Methods, published in 2015 by SIAM. This new book focuses on computational methods developed in the last ten years that make use of splines to approximate functions and data and to solve boundary-value problems. The first half of the book works with bivariate spaces of splines defined on H-triangulations, T-meshes, and curved triangulations. Trivariate tensor-product splines and splines on tetrahedral partitions are also discussed. The second half of the book makes use of these spaces to solve boundary-value problems, with a special emphasis on elliptic PDEs defined on curved domains. The book contains numerous examples and figures to illustrate the methods and their performance. In addition to the included bibliography, a 125-page list of additional references can be downloaded from the SIAM website. All of the algorithms in the book have been coded in MATLAB and are included in a package that can also be downloaded from the website. It can be used to run all of the examples in the book. The package also provides an extensive toolbox of functions that readers can utilize to develop their own spline software. The book is designed for mathematicians, engineers, scientists, and anyone else wanting to make use of spline functions for numerical computation.