Grid Generation And Adaptive Algorithms

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Grid Generation And Adaptive Algorithms

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Author : Marshall W. Bern
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Grid Generation And Adaptive Algorithms written by Marshall W. Bern 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 2012-12-06 with Mathematics categories.

This IMA Volume in Mathematics and its Applications GRID GENERATION AND ADAPTIVE ALGORITHMS is based on the proceedings of a workshop with the same title. The work shop was an integral part of the 1996-97 IMA program on "MATHEMAT ICS IN HIGH-PERFORMANCE COMPUTING. " I would like to thank Marshall Bern (Xerox, Palo Alto Research Cen ter), Joseph E. Flaherty (Department of Computer Science, Rensselaer Polytechnic Institute), and Mitchell Luskin (School of Mathematics, Uni versity of Minnesota), for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Founda tion (NSF), Department of Energy (DOE), and the Army Research Office (ARO), whose financial support made the workshop possible. Willard Miller, Jr. , Professor and Director v PREFACE Scientific and engineering computation has become so complex that traditional numerical computation on uniform meshes is generally not pos sible or too expensive. Mesh generation must reflect both the domain geometry and the expected solution characteristics. Meshes should, fur thermore, be related to the solution through computable estimates of dis cretization errors. This, suggests an automatic and adaptive process where an initial mesh is enriched with the goal of computing a solution with prescribed accuracy specifications in an optimal manner. While automatic mesh generation procedures and adaptive strategies are becoming available, major computational challenges remain. Three-dimensional mesh genera tion is still far from automatic.

Basic Structured Grid Generation

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Author : M Farrashkhalvat
language : en
Publisher: Elsevier
Release Date : 2003-02-11

Basic Structured Grid Generation written by M Farrashkhalvat and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-02-11 with Mathematics categories.

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.

New Challenges In Grid Generation And Adaptivity For Scientific Computing

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Author : Simona Perotto
language : en
Publisher: Springer
Release Date : 2015-04-27

New Challenges In Grid Generation And Adaptivity For Scientific Computing written by Simona Perotto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-27 with Mathematics categories.

This volume collects selected contributions from the “Fourth Tetrahedron Workshop on Grid Generation for Numerical Computations”, which was held in Verbania, Italy in July 2013. The previous editions of this Workshop were hosted by the Weierstrass Institute in Berlin (2005), by INRIA Rocquencourt in Paris (2007), and by Swansea University (2010). This book covers different, though related, aspects of the field: the generation of quality grids for complex three-dimensional geometries; parallel mesh generation algorithms; mesh adaptation, including both theoretical and implementation aspects; grid generation and adaptation on surfaces – all with an interesting mix of numerical analysis, computer science and strongly application-oriented problems.

Next Generation Environmental Models And Computational Methods

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Author : George Delic
language : en
Publisher: SIAM
Release Date : 1997-01-01

Next Generation Environmental Models And Computational Methods written by George Delic and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Technology & Engineering categories.

Large-scale changes are taking place in the way modelling is performed within the US EPA, and a new generation of environmental models is currently under construction. The US EPA is engaging in several modelling efforts in response to Congressional mandates such as the Clean Air Act and the Clean Water Act. These mandates require the scientific modelling of the impact of pollutants on human health and the environment. The complexity of scale in environmental models has increased by several orders of magnitude, with a simultaneous demand for increased stability, accuracy and efficiency in the computed model solution. This book showcases numerical algorithms appropriate to the subject areas listed below and explores how new algorithmic methods would benefit the US EPA's environmental models and other environmental studies.

Grid Generation Methods

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Author : Vladimir D. Liseikin
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-27

Grid Generation Methods written by Vladimir D. Liseikin 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 2009-10-27 with Science categories.

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.

Numerical Geometry Grid Generation And Scientific Computing

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Author : Vladimir A. Garanzha
language : en
Publisher: Springer Nature
Release Date : 2021-09-25

Numerical Geometry Grid Generation And Scientific Computing written by Vladimir A. Garanzha and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-25 with Mathematics categories.

The focus of these conference proceedings is on research, development, and applications in the fields of numerical geometry, scientific computing and numerical simulation, particularly in mesh generation and related problems. In addition, this year’s special focus is on Delaunay triangulations and their applications, celebrating the 130th birthday of Boris Delaunay. In terms of content, the book strikes a balance between engineering algorithms and mathematical foundations. It presents an overview of recent advances in numerical geometry, grid generation and adaptation in terms of mathematical foundations, algorithm and software development and applications. The specific topics covered include: quasi-conformal and quasi-isometric mappings, hyperelastic deformations, multidimensional generalisations of the equidistribution principle, discrete differential geometry, spatial and metric encodings, Voronoi-Delaunay theory for tilings and partitions, duality in mathematical programming and numerical geometry, mesh-based optimisation and optimal control methods. Further aspects examined include iterative solvers for variational problems and algorithm and software development. The applications of the methods discussed are multidisciplinary and include problems from mathematics, physics, biology, chemistry, material science, and engineering.

Advances In Grid Generation

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Author : Olga V. Ushakova
language : en
Publisher:
Release Date : 2007

Advances In Grid Generation written by Olga V. Ushakova and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

Grid generation deals with the use of grids (meshes) in the numerical solution of partial differential equations by finite elements, finite volume, finite differences and boundary elements. Grid generation is applied in the aerospace, mechanical engineering and scientific computing fields. This book presents new research in the field.

Numerical Methods In Multidimensional Radiative Transfer

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Author : Guido Kanschat
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-24

Numerical Methods In Multidimensional Radiative Transfer written by Guido Kanschat 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 2008-12-24 with Mathematics categories.

Traditionally, radiative transfer has been the domain of astrophysicists and climatologists. In nuclear technology one has been dealing with the ana- gous equations of neutron transport. In recent years, applications of radiative transferincombustionmachinedesignandinmedicinebecamemoreandmore important. In all these disciplines one uses the radiative transfer equation to model the formation of the radiation ?eld and its propagation. For slabs and spheres e?ective algorithms for the solution of the transfer equation have been ava- able for quite some time. In addition, the analysis of the equation is quite well developed. Unfortunately, in many modern applications the approximation of a 1D geometry is no longer adequate and one has to consider the full 3D dependencies. This makes the modeling immensely more intricate. The main reasons for the di?culties result from the fact that not only the dimension of the geometric space has to be increased but one also has to employ two angle variables (instead of one) and very often one has to consider frequency coupling (due to motion or redistribution in spectral lines). In actual cal- lations this leads to extremely large matrices which, in addition, are usually badly conditioned and therefore require special care. Analytical solutions are not available except for very special cases. Although radiative transfer problems are interesting also from a ma- ematical point of view, mathematicians have largely neglected the transfer equation for a long time.

Understanding And Implementing The Finite Element Method

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Author : Mark S. Gockenbach
language : en
Publisher: SIAM
Release Date : 2006-01-01

Understanding And Implementing The Finite Element Method written by Mark S. Gockenbach and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-01 with Mathematics categories.

Understanding and Implementing the Finite Element Method Mark S. Gockenbach "Upon completion of this book a student or researcher would be well prepared to employ finite elements for an application problem or proceed to the cutting edge of research in finite element methods. The accuracy and the thoroughness of the book are excellent." --Anthony Kearsley, research mathematician, National Institute of Standards and Technology The infinite element method is the most powerful general-purpose technique for computing accurate solutions to partial differential equations. Understanding and Implementing the Finite Element Method is essential reading for those interested in understanding both the theory and the implementation of the finite element method for equilibrium problems. This book contains a thorough derivation of the finite element equations as well as sections on programming the necessary calculations, solving the finite element equations, and using a posteriori error estimates to produce validated solutions. Accessible introductions to advanced topics, such as multigrid solvers, the hierarchical basis conjugate gradient method, and adaptive mesh generation, are provided. Each chapter ends with exercises to help readers master these topics.

Multiblock Grid Generation

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Author : Nigel P. Weatherill
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Multiblock Grid Generation written by Nigel P. Weatherill 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 2012-12-06 with Technology & Engineering categories.

Computational Fluid Dynamics research, especially for aeronautics, continues to be a rewarding and industrially relevant field of applied science in which to work. An enthusiastic international community of expert CFD workers continue to push forward the frontiers of knowledge in increasing number. Applications of CFD technology in many other sectors of industry are being successfully tackled. The aerospace industry has made significant investments and enjoys considerable benefits from the application of CFD to its products for the last two decades. This era began with the pioneering work ofMurman and others that took us into the transonic (potential flow) regime for the first time in the early 1970's. We have also seen momentous developments of the digital computer in this period into vector and parallel supercomputing. Very significant advances in all aspects of the methodology have been made to the point where we are on the threshold of calculating solutions for the Reynolds-averaged Navier-Stokes equations for complete aircraft configurations. However, significant problems and challenges remain in the areas of physical modelling, numerics and computing technology. The long term industrial requirements are captured in the U. S. Governments 'Grand Challenge' for 'Aerospace Vehicle Design' for the 1990's: 'Massively parallel computing systems and advanced parallel software technology and algorithms will enable the development and validation of multidisciplinary, coupled methods. These methods will allow the numerical simulation and design optimisation of complete aerospace vehicle systems throughout the flight envelope'.