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Author: Vladimir D. Liseikin
Publisher: Springer Science & Business Media
ISBN: 3662054159
Category : Science
Languages : en
Pages : 274
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Book Description
The process of breaking up a physical domain into smaller sub-domains, known as meshing, facilitates the numerical solution of partial differential equations used to simulate physical systems. In an updated and expanded Second Edition, this monograph gives a detailed treatment based on the numerical solution of inverted Beltramian and diffusion equations with respect to monitor metrics for generating both structured and unstructured grids in domains and on surfaces.
Author: Vladimir D. Liseikin
Publisher: Springer Science & Business Media
ISBN: 3662054159
Category : Science
Languages : en
Pages : 274
Get Book Here
Book Description
The process of breaking up a physical domain into smaller sub-domains, known as meshing, facilitates the numerical solution of partial differential equations used to simulate physical systems. In an updated and expanded Second Edition, this monograph gives a detailed treatment based on the numerical solution of inverted Beltramian and diffusion equations with respect to monitor metrics for generating both structured and unstructured grids in domains and on surfaces.
Author: Joe F. Thompson
Publisher: CRC Press
ISBN: 9781420050349
Category : Technology & Engineering
Languages : en
Pages : 1136
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Book Description
Handbook of Grid Generation addresses the use of grids (meshes) in the numerical solutions of partial differential equations by finite elements, finite volume, finite differences, and boundary elements. Four parts divide the chapters: structured grids, unstructured girds, surface definition, and adaption/quality. An introduction to each section provides a roadmap through the material. This handbook covers: Fundamental concepts and approaches Grid generation process Essential mathematical elements from tensor analysis and differential geometry, particularly relevant to curves and surfaces Cells of any shape - Cartesian, structured curvilinear coordinates, unstructured tetrahedra, unstructured hexahedra, or various combinations Separate grids overlaid on one another, communicating data through interpolation Moving boundaries and internal interfaces in the field Resolving gradients and controlling solution error Grid generation codes, both commercial and freeware, as well as representative and illustrative grid configurations Handbook of Grid Generation contains 37 chapters as well as contributions from more than 100 experts from around the world, comprehensively evaluating this expanding field and providing a fundamental orientation for practitioners.
Author: Patrick Knupp
Publisher: CRC Press
ISBN: 0429605307
Category : Mathematics
Languages : en
Pages : 312
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Book Description
Fundamentals of Grid Generation is an outstanding text/reference designed to introduce students in applied mathematics, mechanical engineering, and aerospace engineering to structured grid generation. It provides excellent reference material for practitioners in industry, and it presents new concepts to researchers. Readers will learn what boundary-conforming grids are, how to generate them, and how to devise their own methods. The text is written in a clear, intuitive style that doesn't get bogged down in unnecessary abstractions. Topics covered include planar, surface, and 3-D grid generation; numerical techniques; solution adaptivity; the finite volume approach to discretization of hosted equations; concepts from elementary differential geometry; and the transformation of differential operators to general coordinate systems. The book also reviews the literature on algebraic, conformal, orthogonal, hyperbolic, parabolic, elliptic, biharmonic, and variational approaches to grid generation. This unique volume closes with the author's original methods of variational grid generation.
Author: Vladimir D. Liseikin
Publisher: Springer
ISBN: 3319578464
Category : Science
Languages : en
Pages : 541
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Book Description
This text is an introduction to methods of grid generation technology in scientific computing. Special attention is given to methods developed by the author for the treatment of singularly-perturbed equations, e.g. in modeling high Reynolds number flows. Functionals of conformality, orthogonality, energy and alignment are discussed.
Author: M Farrashkhalvat
Publisher: Elsevier
ISBN: 0080472087
Category : Mathematics
Languages : en
Pages : 242
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Book Description
Finite element, finite volume and finite difference methods use grids to solve the numerous differential equations that arise in the modelling of physical systems in engineering. Structured grid generation forms an integral part of the solution of these procedures. Basic Structured Grid Generation provides the necessary mathematical foundation required for the successful generation of boundary-conforming grids and will be an important resource for postgraduate and practising engineers.The treatment of structured grid generation starts with basic geometry and tensor analysis before moving on to identify the variety of approaches that can be employed in the generation of structured grids. The book then introduces unstructured grid generation by explaining the basics of Delaunay triangulation and advancing front techniques. - A practical, straightforward approach to this complex subject for engineers and students. - A key technique for modelling physical systems.
Author: Herbert Edelsbrunner
Publisher: Cambridge University Press
ISBN: 9780521793094
Category : Computers
Languages : en
Pages : 206
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Book Description
The book combines topics in mathematics (geometry and topology), computer science (algorithms), and engineering (mesh generation). The original motivation for these topics was the difficulty faced (both conceptually and in the technical execution) in any attempt to combine elements of combinatorial and of numerical algorithms. Mesh generation is a topic where a meaningful combination of these different approaches to problem solving is inevitable. The book develops methods from both areas that are amenable to combination, and explains recent breakthrough solutions to meshing that fit into this category.The book should be an ideal graduate text for courses on mesh generation. The specific material is selected giving preference to topics that are elementary, attractive, lend themselves to teaching, useful, and interesting.
Author: Vladimir D. Liseikin
Publisher: Springer Science & Business Media
ISBN: 9048129125
Category : Science
Languages : en
Pages : 390
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Book Description
This text is an introduction to methods of grid generation technology in scientific computing. Special attention is given to methods developed by the author for the treatment of singularly-perturbed equations, e.g. in modeling high Reynolds number flows. Functionals of conformality, orthogonality, energy and alignment are discussed.
Author: Stanislav S. Makhanov
Publisher: Springer Science & Business Media
ISBN: 354071121X
Category : Mathematics
Languages : en
Pages : 206
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Book Description
This book presents new optimization algorithms designed to improve the efficiency of tool paths for five-axis NC machining of sculptured surfaces. The book covers both the structure of the SLAM problem in general and proposes a new extremely efficient approach. It can be used by undergraduate and graduate students and researchers in the field of NC machining and CAD/CAM as well as by corporate research groups for advanced optimization of cutting operations.
Author: Glen A Hansen
Publisher: World Scientific
ISBN: 1783260564
Category : Mathematics
Languages : en
Pages : 533
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Book Description
This book focuses on mesh (grid) enhancement techniques — specifically, the use of selected elliptic methods for both structured and unstructured meshes associated with computational physics applications. Mesh enhancement is the process in which an existing mesh is modified to better meet the requirements of the physics application. To provide the reader with sufficient background information, seven of the nine chapters contain a summary of the numerical simulation process, basic background on mesh terminology and generation approaches, computational geometry, discretization of differential equations, methods of solving linear and nonlinear algebraic systems, geometry of surfaces in Euclidean space, and general elliptic methods for mesh enhancement. Furthermore, these chapters use the concept of harmonic coordinates to develop a unifying framework, the Laplace-Beltrami system, which is the governing principle of the book. The final two chapters apply this scheme, along with other selected elliptic methods, to various structured and unstructured example problems./a
Author: Tian-Xiang Yue
Publisher: CRC Press
ISBN: 9781439817599
Category : Science
Languages : en
Pages : 711
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Book Description
Although GIS provides powerful functionality for spatial analysis, data overlay and storage, these spatially oriented systems lack the ability to represent temporal dynamics, which is a major impediment to its use in surface modeling. However, rapid development of computing technology in recent years has made real-time spatial analysis and real-time data visualization become realizable. Based on newly developed methods, Surface Modeling: High Accuracy and High Speed Methods explores solutions to big-error and slow-efficiency problems, two critical challenges that have long plagued those working in with geographical information system (GIS) and computer-aided design (CAD). By developing high accuracy and high speed methods for surface modeling, the book builds a bridge between the mathematical-oriented theory of surface modeling and the user-oriented application where the user is actually able to retrieve information on the method itself. The author examines a novel method of high accuracy surface modeling (HASM) in terms of the fundamental theorem of surfaces. He then analyzes the coefficient matrix and develops an adaptive method of HASM (HASM-AM), a multi-grade method of HASM (HASM-MG), and an adjustment method of HASM (HASM-AD). He uses numerical tests and real world studies to demonstrate that HASM-AM, HASM-MG, and HASM-AD have highly accelerated computational speed, especially for simulations with huge computational work. Building on this, the book discusses a HASM-based method for dynamic simulation (HASM-FDS), and then applies HASM methods to simulate terrains, climate change, ecosystem change, land cover, and soil properties. It demonstrates HASM's potential for simulating population distribution, human carrying capacity, ecosystem services, ecological diversity, change detection, and wind velocity. The book concludes with a discussion of the problems that exist in surface modeling on a global level and evaluates possible solutions to these problems.
