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Author : Anna Watkins
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (111 download)
Download or read book A Moving Mesh Finite Element Method and Its Application to Population Dynamics written by Anna Watkins and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : G.R. Liu
Publisher : CRC Press
ISBN 13 : 1420040588
Total Pages : 715 pages
Book Rating : 4.4/5 (2 download)
Download or read book Mesh Free Methods written by G.R. Liu and published by CRC Press. This book was released on 2002-07-29 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: As we attempt to solve engineering problems of ever increasing complexity, so must we develop and learn new methods for doing so. The Finite Difference Method used for centuries eventually gave way to Finite Element Methods (FEM), which better met the demands for flexibility, effectiveness, and accuracy in problems involving complex geometry. Now,
Author : Weizhang Huang
Publisher : Springer Science & Business Media
ISBN 13 : 1441979166
Total Pages : 446 pages
Book Rating : 4.4/5 (419 download)
Download or read book Adaptive Moving Mesh Methods written by Weizhang Huang and published by Springer Science & Business Media. This book was released on 2010-10-26 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations. It presents a general framework and theory for adaptive mesh generation and gives a comprehensive treatment of moving mesh methods and their basic components, along with their application for a number of nontrivial physical problems. Many explicit examples with computed figures illustrate the various methods and the effects of parameter choices for those methods. Graduate students, researchers and practitioners working in this area will benefit from this book.
Author : Benjamin Vincent Wells
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (111 download)
Download or read book A Moving Mesh Finite Element Method for the Numerical Solution of Partial Differential Equations and Systems written by Benjamin Vincent Wells and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Viktor A. Rukavishnikov
Publisher : MDPI
ISBN 13 : 3036503765
Total Pages : 128 pages
Book Rating : 4.0/5 (365 download)
Download or read book Mesh Methods written by Viktor A. Rukavishnikov and published by MDPI. This book was released on 2021-03-29 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Pascal Jean Frey
Publisher : Hermes Science Publications
ISBN 13 : 9781903398005
Total Pages : 814 pages
Book Rating : 4.3/5 (98 download)
Download or read book Mesh Generation written by Pascal Jean Frey and published by Hermes Science Publications. This book was released on 2000 with total page 814 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical simulation of physical problems expressed in terms of partial differential equations (so-called PDE's) using a finite element, finite volume, boundary element, or any other numerical method requires the discretization of the domain of interest into a set of elements, i.e. a mesh. The differential equations are approximated by a set of algebraic equations on this mesh, this set being then solved to provide the approximate solution of the partial differential system over the field. The discretization requires certain properties for the solution to be exploitable and must at least conform to all domain boundaries in order to accurately represent boundary conditions. Consequently, the mesh generation stage, as an essential pre-requisite, is of utmost importance in the computational schemes, as it is related to the convergence of the computational scheme as well as to the accuracy of the numerical solutions. There is indeed a variety of algorithms suitable to produce such meshes. Some of these methods are designed to handle specific geometric situations while others can be used in a more general context. User-driven, semi-automatic as well as fully automatic methods exist leading to structured, unstructured or mixed meshes. The mesh generation problems are mainly related to the boundary meshing (line, curve and surface meshing) and domain meshing issues (planar domain or volumetric domain). Numerous computational issues must be carefully addressed for designing reliable and robust meshing algorithms. These issues concern computer-related data structures and algorithms (low-level routines) as well as advanced data structures and computational schemes (high-level routines). In this regard, basic computational tools, geometric and discrete geometric notions, computational and mesh data structures, element and mesh definitions are of significant importance. The aim of this book is to provide a comprehensive survey of the different algorithms and data structures useful for triangulation and meshing construction. In addition, several aspects will also be described, for instance mesh modification tools, mesh evaluation criteria, mesh optimization, including even adaptive mesh construction as well as parallel meshing techniques.
Author : Dimitris P. Vartziotis
Publisher : CRC Press
ISBN 13 : 0429680104
Total Pages : 254 pages
Book Rating : 4.4/5 (296 download)
Download or read book The GETMe Mesh Smoothing Framework written by Dimitris P. Vartziotis and published by CRC Press. This book was released on 2018-12-07 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: High quality meshes play a key role in many applications based on digital modeling and simulation. The finite element method is a paragon for such an approach and it is well known that quality meshes can significantly improve computational efficiency and solution accuracy of this method. Therefore, a lot of effort has been put in methods for improving mesh quality. These range from simple geometric approaches, like Laplacian smoothing, with a high computational efficiency but possible low resulting mesh quality, to global optimization-based methods, resulting in an excellent mesh quality at the cost of an increased computational and implementational complexity. The geometric element transformation method (GETMe) aims to fill the gap between these two approaches. It is based on geometric mesh element transformations, which iteratively transform polygonal and polyhedral elements into their regular counterparts or into elements with a prescribed shape. GETMe combines a Laplacian smoothing-like computational efficiency with a global optimization-like effectiveness. The method is straightforward to implement and its variants can also be used to improve tangled and anisotropic meshes. This book describes the mathematical theory of geometric element transformations as foundation for mesh smoothing. It gives a thorough introduction to GETMe-based mesh smoothing and its algorithms providing a framework to focus on effectively improving key mesh quality aspects. It addresses the improvement of planar, surface, volumetric, mixed, isotropic, and anisotropic meshes and addresses aspects of combining mesh smoothing with topological mesh modification. The advantages of GETMe-based mesh smoothing are demonstrated by the example of various numerical tests. These include smoothing of real world meshes from engineering applications as well as smoothing of synthetic meshes for demonstrating key aspects of GETMe-based mesh improvement. Results are compared with those of other smoothing methods in terms of runtime behavior, mesh quality, and resulting finite element solution efficiency and accuracy. Features: • Helps to improve finite element mesh quality by applying geometry-driven mesh smoothing approaches. • Supports the reader in understanding and implementing GETMe-based mesh smoothing. • Discusses aspects and properties of GETMe smoothing variants and thus provides guidance for choosing the appropriate mesh improvement algorithm. • Addresses smoothing of various mesh types: planar, surface, volumetric, isotropic, anisotropic, non-mixed, and mixed. • Provides and analyzes geometric element transformations for polygonal and polyhedral elements with regular and non-regular limits. • Includes a broad range of numerical examples and compares results with those of other smoothing methods.
Author : G.R. LIU
Publisher : CRC Press
ISBN 13 : 9781138372702
Total Pages : 792 pages
Book Rating : 4.3/5 (727 download)
Download or read book Meshfree Methods written by G.R. LIU and published by CRC Press. This book was released on 2018-09-10 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understand How to Use and Develop Meshfree Techniques An Update of a Groundbreaking Work Reflecting the significant advances made in the field since the publication of its predecessor, Meshfree Methods: Moving Beyond the Finite Element Method, Second Edition systematically covers the most widely used meshfree methods. With 70% new material, this edition addresses important new developments, especially on essential theoretical issues. New to the Second Edition Much more details on fundamental concepts and important theories for numerical methods Discussions on special properties of meshfree methods, including stability, convergence, accurate, efficiency, and bound property More detailed discussion on error estimation and adaptive analysis using meshfree methods Developments on combined meshfree/finite element method (FEM) models Comparison studies using meshfree and FEM Drawing on the author's own research, this book provides a single-source guide to meshfree techniques and theories that can effectively handle a variety of complex engineering problems. It analyzes how the methods work, explains how to use and develop the methods, and explores the problems associated with meshfree methods. To access MFree2D (copyright, G. R. Liu), which accompanies MESHFREE METHODS: MOVING BEYOND THE FINITE ELEMENT METHOD, Second Edition (978-1-4200-8209-8) by Dr. G. R. Liu, please go to the website: www.ase.uc.edu/ liugr An access code is needed to use program - to receive it please email Dr. Liu directly at: [email protected] Dr. Liu will reply to you directly with the code, and you can then proceed to use the software.
Author : Daniel S.H. Lo
Publisher : CRC Press
ISBN 13 : 041569048X
Total Pages : 676 pages
Book Rating : 4.4/5 (156 download)
Download or read book Finite Element Mesh Generation written by Daniel S.H. Lo and published by CRC Press. This book was released on 2015-01-15 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: Highlights the Progression of Meshing Technologies and Their Applications Finite Element Mesh Generation provides a concise and comprehensive guide to the application of finite element mesh generation over 2D domains, curved surfaces, and 3D space. Organised according to the geometry and dimension of the problem domains, it develops from the basic meshing algorithms to the most advanced schemes to deal with problems with specific requirements such as boundary conformity, adaptive and anisotropic elements, shape qualities, and mesh optimization. It sets out the fundamentals of popular techniques, including: Delaunay triangulation Advancing-front (ADF) approach Quadtree/Octree techniques Refinement and optimization-based strategies From the geometrical and the topological aspects and their associated operations and inter-relationships, each approach is vividly described and illustrated with examples. Beyond the algorithms, the book also explores the practice of using metric tensor and surface curvatures for generating anisotropic meshes on parametric space. It presents results from research including 3D anisotropic meshing, mesh generation over unbounded domains, meshing by means of intersection, re-meshing by Delaunay-ADF approach, mesh refinement and optimization, generation of hexahedral meshes, and large scale and parallel meshing, along with innovative unpublished meshing methods. The author provides illustrations of major meshing algorithms, pseudo codes, and programming codes in C++ or FORTRAN. Geared toward research centers, universities, and engineering companies, Finite Element Mesh Generation describes mesh generation methods and fundamental techniques, and also serves as a valuable reference for laymen and experts alike.
Author : P. L. George
Publisher : Wiley
ISBN 13 : 9780471930976
Total Pages : 344 pages
Book Rating : 4.9/5 (39 download)
Download or read book Automatic Mesh Generation written by P. L. George and published by Wiley. This book was released on 1992-01-30 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mesh generation is a necessary prerequisite for the numerical analysis of engineering problems--both geometrically complicated and large size. With an increasing need for automatic applications to accomplish these complicated tasks, it offers an in-depth survey of existing techniques for mesh generation. A number of problems are given and their solutions carefully explained. Also includes detailed coverage of traditional structured grids along with unstructured meshes of triangles and tetrahedra.
Author : Rubén Sevilla
Publisher : Springer Nature
ISBN 13 : 3030925404
Total Pages : 328 pages
Book Rating : 4.0/5 (39 download)
Download or read book Mesh Generation and Adaptation written by Rubén Sevilla and published by Springer Nature. This book was released on 2022-05-18 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The developments in mesh generation are usually driven by the needs of new applications and/or novel algorithms. The last decade has seen a renewed interest in mesh generation and adaptation by the computational engineering community, due to the challenges introduced by complex industrial problems.Another common challenge is the need to handle complex geometries. Nowadays, it is becoming obvious that geometry should be persistent throughout the whole simulation process. Several methodologies that can carry the geometric information throughout the simulation stage are available, but due to the novelty of these methods, the generation of suitable meshes for these techniques is still the main obstacle for the industrial uptake of this technology.This book will cover different aspects of mesh generation and adaptation, with particular emphasis on cutting-edge mesh generation techniques for advanced discretisation methods and complex geometries.
Author : Zhijun Tan
Publisher :
ISBN 13 :
Total Pages : 246 pages
Book Rating : 4.:/5 (69 download)
Download or read book Moving Mesh Finite Volume Method and Its Applications written by Zhijun Tan and published by . This book was released on 2005 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Matthew Maxwell McCoy
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (126 download)
Download or read book Moving Mesh Finite Element Method for Time Dependent Convection-Diffusion Problems written by Matthew Maxwell McCoy and published by . This book was released on 2021 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: The moving mesh finite element method (MM-FEM) has been a significant force in numerically approximating solutions to differential equations that otherwise exhibit spurious, artificial oscillations. This is especially true for singularly perturbed convection-diffusion problems. In the presence of vanishing molecular diffusivity, MM- FEM may not suffice. The numerical method may exhibit under-diffusive properties and other methods need to be integrated into the classic Galerkin formulation. We implement the so-called streamline upwind Petrov-Galerkin method into the adaptive moving mesh method. In particular, we investigate the computation of so-called enhanced diffusivity for spatiotemporal periodic turbulent flows. We look at the case of Brownian tracer particles, i.e. negligible inertial effects. These types of passive advection-diffusion models are used in atmospheric models with turbulent diffusion, so-called Benard-advection cells, and porous materials, along with many other areas of science and engineering. As molecular diffusivity decreases, interior and boundary layers propagate along the streamlines. Once spurious oscillations are present, they too will propagate along the streamlines. Thus, specialized numerical methods are needed in order to resolve these areas of the domain where large gradients are present. The discrete maximum principle is also investigated for general anisotropic time dependent convection-diffusion equations. We obtain lower and upper bounds for time steps as well as obtain conditions on the mass and stiffness matrices resulting from the SUPG formulation. Our approach depends on two meshes and taking into consideration two diffusion matrices and applying metric intersection.
Author :
Publisher :
ISBN 13 :
Total Pages : 704 pages
Book Rating : 4.:/5 (31 download)
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Slimane Adjerid
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (115 download)
Download or read book A moving mesh finite element method with local refinement for parabolic partial differential equations written by Slimane Adjerid and published by . This book was released on 1985 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard Andrew Norton
Publisher :
ISBN 13 :
Total Pages : 135 pages
Book Rating : 4.:/5 (156 download)
Download or read book Various Moving Mesh Methods written by Richard Andrew Norton and published by . This book was released on 2005 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: As well as presenting the basic finite element method, this thesis presents two adaptive moving mesh methods: the moving finite element method and a class of methods based on the equidistribution principle, the so called moving mesh partial differential equations. One and two dimensional examples are given for the finite element and moving finite element methods and the one dimensional Burger's equation is successfully solved using the moving mesh partial differential equations. The code for the computer programs, written in C, that solve all the example problems is also given.
Author : Paul L. George
Publisher :
ISBN 13 :
Total Pages : 356 pages
Book Rating : 4.F/5 ( download)
Download or read book Automatic Mesh Generation written by Paul L. George and published by . This book was released on 1991 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
