Kernel Based Meshless Methods

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Kernel-based Approximation Methods Using Matlab

Author : Gregory E Fasshauer
Publisher : World Scientific Publishing Company
ISBN 13 : 9814630152
Total Pages : 537 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Kernel-based Approximation Methods Using Matlab by : Gregory E Fasshauer

Download or read book Kernel-based Approximation Methods Using Matlab written by Gregory E Fasshauer and published by World Scientific Publishing Company. This book was released on 2015-07-30 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Meshfree Approximation Methods with MATLAB

Author : Gregory E. Fasshauer
Publisher : World Scientific
ISBN 13 : 981270633X
Total Pages : 520 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Meshfree Approximation Methods with MATLAB by : Gregory E. Fasshauer

Download or read book Meshfree Approximation Methods with MATLAB written by Gregory E. Fasshauer and published by World Scientific. This book was released on 2007 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Meshless Methods in Solid Mechanics

Author : Youping Chen
Publisher : Springer Science & Business Media
ISBN 13 : 0387333681
Total Pages : 211 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Meshless Methods in Solid Mechanics by : Youping Chen

Download or read book Meshless Methods in Solid Mechanics written by Youping Chen and published by Springer Science & Business Media. This book was released on 2006-12-31 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the fundamentals of continuum mechanics, the integral formulation methods of continuum problems, the basic concepts of finite element methods, and the methodologies, formulations, procedures, and applications of various meshless methods. It also provides general and detailed procedures of meshless analysis on elastostatics, elastodynamics, non-local continuum mechanics and plasticity with a large number of numerical examples. Some basic and important mathematical methods are included in the Appendixes. For readers who want to gain knowledge through hands-on experience, the meshless programs for elastostatics and elastodynamics are provided on an included disc.

Meshfree Methods for Partial Differential Equations

Author : Michael Griebel
Publisher : Springer Science & Business Media
ISBN 13 : 3642561039
Total Pages : 468 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Meshfree Methods for Partial Differential Equations by : Michael Griebel

Download or read book Meshfree Methods for Partial Differential Equations written by Michael Griebel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact that meshfree discretizations and particle models are often better suited to cope with geometric changes of the domain of interest, e.g. free surfaces and large deformations, than classical discretization techniques such as finite differences, finite elements or finite volumes. Another obvious advantage of meshfree discretizations is their independence of a mesh so that the costs of mesh generation are eliminated. Also, the treatment of time-dependent PDEs from a Lagrangian point of view and the coupling of particle models and continuous models gained enormous interest in recent years from a theoretical as well as from a practial point of view. This volume consists of articles which address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM etc.) and their application in applied mathematics, physics and engineering.

Progress on Meshless Methods

Author : A. J. M. Ferreira
Publisher : Springer Science & Business Media
ISBN 13 : 1402088213
Total Pages : 311 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Progress on Meshless Methods by : A. J. M. Ferreira

Download or read book Progress on Meshless Methods written by A. J. M. Ferreira and published by Springer Science & Business Media. This book was released on 2008-11-23 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years meshless/meshfree methods have gained considerable attention in engineering and applied mathematics. The variety of problems that are now being addressed by these techniques continues to expand and the quality of the results obtained demonstrates the effectiveness of many of the methods currently available. The book presents a significant sample of the state of the art in the field with methods that have reached a certain level of maturity while also addressing many open issues. The book collects extended original contributions presented at the Second ECCOMAS Conference on Meshless Methods held in 2007 in Porto. The list of contributors reveals a fortunate mix of highly distinguished authors as well as quite young but very active and promising researchers, thus giving the reader an interesting and updated view of different meshless approximation methods and their range of applications. The material presented is appropriate for researchers, engineers, physicists, applied mathematicians and graduate students interested in this active research area.

The Meshless Local Petrov-Galerkin (MLPG) Method

Author : Satya N. Atluri
Publisher : Crest
ISBN 13 :
Total Pages : 448 pages
Book Rating : 4.X/5 (4 download)

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Book Synopsis The Meshless Local Petrov-Galerkin (MLPG) Method by : Satya N. Atluri

Download or read book The Meshless Local Petrov-Galerkin (MLPG) Method written by Satya N. Atluri and published by Crest. This book was released on 2002 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Meshless Methods and Their Numerical Properties

Author : Hua Li
Publisher : CRC Press
ISBN 13 : 1466517476
Total Pages : 429 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Meshless Methods and Their Numerical Properties by : Hua Li

Download or read book Meshless Methods and Their Numerical Properties written by Hua Li and published by CRC Press. This book was released on 2013-02-22 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meshless, or meshfree methods, which overcome many of the limitations of the finite element method, have achieved significant progress in numerical computations of a wide range of engineering problems. A comprehensive introduction to meshless methods, Meshless Methods and Their Numerical Properties gives complete mathematical formulations for the m

An Introduction to Meshfree Methods and Their Programming

Author : G.R. Liu
Publisher : Springer Science & Business Media
ISBN 13 : 1402034687
Total Pages : 497 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis An Introduction to Meshfree Methods and Their Programming by : G.R. Liu

Download or read book An Introduction to Meshfree Methods and Their Programming written by G.R. Liu and published by Springer Science & Business Media. This book was released on 2005-12-05 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Scattered Data Approximation

Author : Holger Wendland
Publisher : Cambridge University Press
ISBN 13 : 9781139456654
Total Pages : 346 pages
Book Rating : 4.4/5 (566 download)

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Book Synopsis Scattered Data Approximation by : Holger Wendland

Download or read book Scattered Data Approximation written by Holger Wendland and published by Cambridge University Press. This book was released on 2004-12-13 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity. The book starts with an overview on typical applications of scattered data approximation, coming from surface reconstruction, fluid-structure interaction, and the numerical solution of partial differential equations. It then leads the reader from basic properties to the current state of research, addressing all important issues, such as existence, uniqueness, approximation properties, numerical stability, and efficient implementation. Each chapter ends with a section giving information on the historical background and hints for further reading. Complete proofs are included, making this perfectly suited for graduate courses on multivariate approximation and it can be used to support courses in computer-aided geometric design, and meshless methods for partial differential equations.

Polyharmonic Functions

Author : Nachman Aronszajn
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 290 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Polyharmonic Functions by : Nachman Aronszajn

Download or read book Polyharmonic Functions written by Nachman Aronszajn and published by Oxford University Press, USA. This book was released on 1983 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Acta Numerica 2006: Volume 15

Author : Arieh Iserles
Publisher : Cambridge University Press
ISBN 13 : 9780521868150
Total Pages : 658 pages
Book Rating : 4.8/5 (681 download)

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Book Synopsis Acta Numerica 2006: Volume 15 by : Arieh Iserles

Download or read book Acta Numerica 2006: Volume 15 written by Arieh Iserles and published by Cambridge University Press. This book was released on 2006-08-03 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: A high-impact factor, prestigious annual publication containing invited surveys by subject leaders: essential reading for all practitioners and researchers.

Computational Finite Element Methods in Nanotechnology

Author : Sarhan M. Musa
Publisher : CRC Press
ISBN 13 : 1439893268
Total Pages : 640 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Computational Finite Element Methods in Nanotechnology by : Sarhan M. Musa

Download or read book Computational Finite Element Methods in Nanotechnology written by Sarhan M. Musa and published by CRC Press. This book was released on 2017-12-19 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Finite Element Methods in Nanotechnology demonstrates the capabilities of finite element methods in nanotechnology for a range of fields. Bringing together contributions from researchers around the world, it covers key concepts as well as cutting-edge research and applications to inspire new developments and future interdisciplinary research. In particular, it emphasizes the importance of finite element methods (FEMs) for computational tools in the development of efficient nanoscale systems. The book explores a variety of topics, including: A novel FE-based thermo-electrical-mechanical-coupled model to study mechanical stress, temperature, and electric fields in nano- and microelectronics The integration of distributed element, lumped element, and system-level methods for the design, modeling, and simulation of nano- and micro-electromechanical systems (N/MEMS) Challenges in the simulation of nanorobotic systems and macro-dimensions The simulation of structures and processes such as dislocations, growth of epitaxial films, and precipitation Modeling of self-positioning nanostructures, nanocomposites, and carbon nanotubes and their composites Progress in using FEM to analyze the electric field formed in needleless electrospinning How molecular dynamic (MD) simulations can be integrated into the FEM Applications of finite element analysis in nanomaterials and systems used in medicine, dentistry, biotechnology, and other areas The book includes numerous examples and case studies, as well as recent applications of microscale and nanoscale modeling systems with FEMs using COMSOL Multiphysics® and MATLAB®. A one-stop reference for professionals, researchers, and students, this is also an accessible introduction to computational FEMs in nanotechnology for those new to the field.

Computational Methods

Author : G.R. Liu
Publisher : Springer Science & Business Media
ISBN 13 : 1402039530
Total Pages : 954 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Computational Methods by : G.R. Liu

Download or read book Computational Methods written by G.R. Liu and published by Springer Science & Business Media. This book was released on 2007-05-26 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: The First International Conference on Computational Methods (ICCM04), organized by the department of Mechanical Engineering, National University of Singapore, was held in Singapore, December 15-17, 2004, with great success. This conference proceedings contains some 290 papers from more than 30 countries/regions. The papers cover a broad range of topics such as meshfree particle methods, Generalized FE and Extended FE methods, inverse analysis and optimization methods. Computational methods for geomechanics, machine learning, vibration, shock, impact, health monitoring, material modeling, fracture and damage mechanics, multi-physics and multi-scales simulation, sports and environments are also included. All the papers are pre-reviewed before they are accepted for publication in this proceedings. The proceedings will provide an informative, timely and invaluable resource for engineers and scientists working in the important areas of computational methods.

Computational Mechanics

Author : Zhenhan Yao
Publisher : 清华大学出版社有限公司
ISBN 13 : 9787302093428
Total Pages : 608 pages
Book Rating : 4.0/5 (934 download)

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Book Synopsis Computational Mechanics by : Zhenhan Yao

Download or read book Computational Mechanics written by Zhenhan Yao and published by 清华大学出版社有限公司. This book was released on 2004 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advances In Meshfree And X-fem Methods (Vol 2) - With Cd-rom, Proceedings Of The 1st Asian Workshop On Meshfree Methods

Author : Gui-rong Liu
Publisher : World Scientific
ISBN 13 : 9814486884
Total Pages : 274 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Advances In Meshfree And X-fem Methods (Vol 2) - With Cd-rom, Proceedings Of The 1st Asian Workshop On Meshfree Methods by : Gui-rong Liu

Download or read book Advances In Meshfree And X-fem Methods (Vol 2) - With Cd-rom, Proceedings Of The 1st Asian Workshop On Meshfree Methods written by Gui-rong Liu and published by World Scientific. This book was released on 2002-12-16 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of the papers from the proceedings of the 1st Asian Workshop on Meshfree Methods held in conjunction with the 2nd International Conference on Structural Stability & Dynamics (ICSSD02) on 16-18 December 2002 in Singapore. It contains 36 articles covering most of the topics in the rapidly developing areas of meshfree methods and extended finite element methods (X-FEM). These topics include domain discretization, boundary discretization, combined domain/boundary discretization, meshfree particle methods, collocation methods, X-FEM, etc. Papers on issues related to implementation and coding of meshfree methods are also presented. The areas of applications of meshfree methods include solving general partial differential equations, the mechanics of solids and structures, smart material/structures, soil-structures, fracture mechanics, fluid dynamics, impact, penetration, micro-fluidics, etc. In addition, techniques for field variable interpolation, such as the moving least squares (MLS) approximation, the point interpolation method (PIM), and radial PIM are reported.

Meshfree and Particle Methods

Author : Ted Belytschko
Publisher : John Wiley & Sons
ISBN 13 : 0470848006
Total Pages : 357 pages
Book Rating : 4.4/5 (78 download)

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Book Synopsis Meshfree and Particle Methods by : Ted Belytschko

Download or read book Meshfree and Particle Methods written by Ted Belytschko and published by John Wiley & Sons. This book was released on 2024-02-27 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides thorough coverage of essential concepts and state-of-the-art developments in the field Meshfree and Particle Methods is the first book of its kind to combine comprehensive, up-to-date information on the fundamental theories and applications of meshfree methods with systematic guidance on practical coding implementation. Broad in scope and content, this unique volume provides readers with the knowledge necessary to perform research and solve challenging problems in nearly all fields of science and engineering using meshfree computational techniques. The authors provide detailed descriptions of essential issues in meshfree methods, as well as specific techniques to address them, while discussing a wide range of subjects and use cases. Topics include approximations in meshfree methods, nonlinear meshfree methods, essential boundary condition enforcement, quadrature in meshfree methods, strong form collocation methods, and more. Throughout the book, topics are integrated with descriptions of computer implementation and an open-source code (with a dedicated chapter for users) to illustrate the connection between the formulations discussed in the text and their real-world implementation and application. This authoritative resource: Explains the fundamentals of meshfree methods, their constructions, and their unique capabilities as compared to traditional methods Features an overview of the open-source meshfree code RKPM2D, including code and numerical examples Describes all the variational concepts required to solve scientific and engineering problems using meshfree methods such as Nitsche’s method and the Lagrange multiplier method Includes comprehensive reviews of essential boundary condition enforcement, quadrature in meshfree methods, and nonlinear aspects of meshfree analysis Discusses other Galerkin meshfree methods, strong form meshfree methods, and their comparisons Meshfree and Particle Methods: Fundamentals and Applications is the perfect introduction to meshfree methods for upper-level students in advanced numerical analysis courses, and is an invaluable reference for professionals in mechanical, aerospace, civil, and structural engineering, and related fields, who want to understand and apply these concepts directly, or effectively use commercial and other production meshfree and particle codes in their work.

Meshfree Methods for Partial Differential Equations VII

Author : Michael Griebel
Publisher : Springer
ISBN 13 : 3319068989
Total Pages : 323 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Meshfree Methods for Partial Differential Equations VII by : Michael Griebel

Download or read book Meshfree Methods for Partial Differential Equations VII written by Michael Griebel and published by Springer. This book was released on 2014-12-02 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meshfree methods, particle methods, and generalized finite element methods have witnessed substantial development since the mid 1990s. The growing interest in these methods is due in part to the fact that they are extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. Furthermore, meshfree methods offer a number of advantageous features which are especially attractive when dealing with multiscale phenomena: a priori knowledge about particular local behavior of the solution can easily be introduced in the meshfree approximation space, and coarse-scale approximations can be seamlessly refined with fine-scale information. This volume collects selected papers presented at the Seventh International Workshop on Meshfree Methods, held in Bonn, Germany in September 2013. They address various aspects of this highly dynamic research field and cover topics from applied mathematics, physics and engineering.