Author : Bo-nan Jiang
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 19,81 MB
Release : 1998-06-22
Category : Computers
ISBN : 9783540639343
This is the first monograph on the subject, providing a comprehensive introduction to the LSFEM method for numerical solution of PDEs. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics.
Author : Pavel B. Bochev
Publisher : Springer Science & Business Media
Page : 669 pages
File Size : 28,59 MB
Release : 2009-04-28
Category : Mathematics
ISBN : 0387689222
Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.
Author : Karan S. Surana
Publisher : CRC Press
Page : 824 pages
File Size : 37,52 MB
Release : 2016-11-17
Category : Science
ISBN : 1498780512
Written by two well-respected experts in the field, The Finite Element Method for Boundary Value Problems: Mathematics and Computations bridges the gap between applied mathematics and application-oriented computational studies using FEM. Mathematically rigorous, the FEM is presented as a method of approximation for differential operators that are mathematically classified as self-adjoint, non-self-adjoint, and non-linear, thus addressing totality of all BVPs in various areas of engineering, applied mathematics, and physical sciences. These classes of operators are utilized in various methods of approximation: Galerkin method, Petrov-Galerkin Method, weighted residual method, Galerkin method with weak form, least squares method based on residual functional, etc. to establish unconditionally stable finite element computational processes using calculus of variations. Readers are able to grasp the mathematical foundation of finite element method as well as its versatility of applications. h-, p-, and k-versions of finite element method, hierarchical approximations, convergence, error estimation, error computation, and adaptivity are additional significant aspects of this book.
Author : Bo-nan Jiang
Publisher : Springer Science & Business Media
Page : 425 pages
File Size : 45,39 MB
Release : 2013-03-14
Category : Science
ISBN : 3662037408
This is the first monograph on the subject, providing a comprehensive introduction to the LSFEM method for numerical solution of PDEs. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics.
Author : Susanne Brenner
Publisher : Springer Science & Business Media
Page : 369 pages
File Size : 22,65 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 1475736584
A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain decomposition algorithms; Second edition contains two new chapters, as well as many new exercises; Previous edition sold over 3000 copies worldwide
Author : Mats G. Larson
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 46,75 MB
Release : 2013-01-13
Category : Computers
ISBN : 3642332870
This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.
Author : John Wolberg
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 30,31 MB
Release : 2006-02-08
Category : Mathematics
ISBN : 3540317201
Develops the full power of the least-squares method Enables engineers and scientists to apply the method to their specific problem Deals with linear as well as with non-linear least-squares, parametric as well as non-parametric methods
Author : P. SESHU
Publisher : PHI Learning Pvt. Ltd.
Page : 340 pages
File Size : 13,76 MB
Release : 2003-01-01
Category : Mathematics
ISBN : 8120323157
Designed for a one-semester course in Finite Element Method, this compact and well-organized text presents FEM as a tool to find approximate solutions to differential equations. This provides the student a better perspective on the technique and its wide range of applications. This approach reflects the current trend as the present-day applications range from structures to biomechanics to electromagnetics, unlike in conventional texts that view FEM primarily as an extension of matrix methods of structural analysis. After an introduction and a review of mathematical preliminaries, the book gives a detailed discussion on FEM as a technique for solving differential equations and variational formulation of FEM. This is followed by a lucid presentation of one-dimensional and two-dimensional finite elements and finite element formulation for dynamics. The book concludes with some case studies that focus on industrial problems and Appendices that include mini-project topics based on near-real-life problems. Postgraduate/Senior undergraduate students of civil, mechanical and aeronautical engineering will find this text extremely useful; it will also appeal to the practising engineers and the teaching community.
Author : G.R. Liu
Publisher : Springer Science & Business Media
Page : 497 pages
File Size : 32,15 MB
Release : 2005-12-05
Category : Technology & Engineering
ISBN : 1402034687
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.
Author : Seiichi Koshizuka
Publisher : Academic Press
Page : 307 pages
File Size : 37,15 MB
Release : 2018-06-01
Category : Science
ISBN : 0128128372
Moving Particle Semi-implicit Method: A Meshfree Particle Method for Fluid Dynamics begins by familiarizing the reader with basic theory that supports their journey through sections on advanced MPH methods. The unique insights that this method provides include fluid-structure interaction, non-Newtonian flow, and cavitation, making it relevant to a wide range of applications in the mechanical, structural, and nuclear industries, and in bioengineering. Co-authored by the originator of the MPS method, this book is the most authoritative guide available. It will be of great value to students, academics and researchers in industry. - Presents the differences between MPH and SPH, helping readers choose between methods for different purposes - Provides pieces of computer code that readers can use in their own simulations - Includes the full, extended algorithms - Explores the use of MPS in a range of industries and applications, including practical advice
