Adaptive Moving Mesh Methods / Weizhang Huang (2011)  

Público ISBD Título : Adaptive Moving Mesh Methods Tipo de documento: documento electrónico Autores: Weizhang Huang ; SpringerLink (Online service) ; Robert D. Russell Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 174 Número de páginas: XVIII, 434 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-7916-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Partial  differential  equations  Computer  mathematics  Numerical  analysis  Analysis  Computational  and  Differential  Equations Clasificación: 51 Matemáticas Resumen: Moving mesh methods are an effective, mesh-adaptation-based approach for the numerical solution of mathematical models of physical phenomena. Currently there exist three main strategies for mesh adaptation, namely, to use mesh subdivision,  local high order approximation (sometimes combined with mesh subdivision), and mesh movement. The latter type of adaptive mesh method has been less well studied, both computationally and theoretically. 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. The partial differential equations considered are mainly parabolic (diffusion-dominated, rather  than convection-dominated). The extensive bibliography provides an invaluable guide to the literature in this field. Each chapter contains useful exercises. Graduate students, researchers and practitioners working in this area will benefit from this book. Weizhang Huang is a Professor in the Department of Mathematics at the University of Kansas. Robert D. Russell is a Professor in the Department of Mathematics at Simon Fraser University Nota de contenido: Preface -- Introduction -- Adaptive Mesh Movement in 1D -- Discretization of PDEs on Time-Varying Meshes -- Basic Principles of Multidimensional Mesh Adaption -- Monitor Functions -- Variational Mesh Adaptive Methods -- Velocity-Based Adaptive Methods -- Appendix: Sobolev Spaces -- Appendix: Arithmetic Mean Geometric Mean Inequality and Jensen's Inequality -- Bibliography En línea: http://dx.doi.org/10.1007/978-1-4419-7916-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33175 Adaptive Moving Mesh Methods [documento electrónico] / Weizhang Huang ; SpringerLink (Online service) ; Robert D. Russell . - New York, NY : Springer New York, 2011 . - XVIII, 434 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 174) . ISBN : 978-1-4419-7916-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Partial  differential  equations  Computer  mathematics  Numerical  analysis  Analysis  Computational  and  Differential  Equations Clasificación: 51 Matemáticas Resumen: Moving mesh methods are an effective, mesh-adaptation-based approach for the numerical solution of mathematical models of physical phenomena. Currently there exist three main strategies for mesh adaptation, namely, to use mesh subdivision,  local high order approximation (sometimes combined with mesh subdivision), and mesh movement. The latter type of adaptive mesh method has been less well studied, both computationally and theoretically. 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. The partial differential equations considered are mainly parabolic (diffusion-dominated, rather  than convection-dominated). The extensive bibliography provides an invaluable guide to the literature in this field. Each chapter contains useful exercises. Graduate students, researchers and practitioners working in this area will benefit from this book. Weizhang Huang is a Professor in the Department of Mathematics at the University of Kansas. Robert D. Russell is a Professor in the Department of Mathematics at Simon Fraser University Nota de contenido: Preface -- Introduction -- Adaptive Mesh Movement in 1D -- Discretization of PDEs on Time-Varying Meshes -- Basic Principles of Multidimensional Mesh Adaption -- Monitor Functions -- Variational Mesh Adaptive Methods -- Velocity-Based Adaptive Methods -- Appendix: Sobolev Spaces -- Appendix: Arithmetic Mean Geometric Mean Inequality and Jensen's Inequality -- Bibliography En línea: http://dx.doi.org/10.1007/978-1-4419-7916-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33175

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Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration / SpringerLink (Online service) ; Torsten Möller ; Bernd Hamann ; Robert D. Russell (2009)  

Público ISBD Título : Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Torsten Möller ; Bernd Hamann ; Robert D. Russell Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2009 Colección: Mathematics and Visualization, ISSN 1612-3786 Número de páginas: X, 350 p. 183 illus., 134 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-540-49926-8 Idioma : Inglés (eng) Palabras clave: Computer  science  Computers  Mathematics  graphics  Application  software  mathematics  Science  Applications  Theory  of  Computation  Computational  and  Numerical  Analysis  Graphics  Computing  Engineering Clasificación: 51 Matemáticas Resumen: Visualization is one of the most active and exciting areas of Mathematics and Computing Science, and indeed one which is only beginning to mature. Current visualization algorithms break down for very large data sets. While present approaches use multi-resolution ideas, future data sizes will not be handled that way. New algorithms based on sophisticated mathematical modeling techniques must be devised which will permit the extraction of high-level topological structures that can be visualized. For these reasons a workshop was organized at the Banff International Research Station, focused specifically on mathematical issues. A primary objective of the workshop was to gather together a diverse set of researchers in the mathematical areas relevant to the recent advances in order to discuss the research challenges facing this field in the next several years. The workshop was organized into five different thrusts: - Topology and Discrete Methods - Signal and Geometry Processing - Partial Differential Equations - Data Approximation Techniques - Massive Data Applications This book presents a summary of the research ideas presented at this workshop Nota de contenido: Maximizing Adaptivity in Hierarchical Topological Models Using Cancellation Trees -- The TOPORRERY: computation and presentation of multi-resolution topology -- Isocontour based Visualization of Time-varying Scalar Fields -- DeBruijn Counting for Visualization Algorithms -- Topological Methods for Visualizing Vortical Flows -- Stability and Computation of Medial Axes - a State-of-the-Art Report -- Local Geodesic Parametrization: an Ant’s Perspective -- Tensor-Fields Visualization Using a Fabric-like Texture Applied to Arbitrary Two-dimensional Surfaces -- Flow Visualization via Partial Differential Equations -- Iterative Twofold Line Integral Convolution for Texture-Based Vector Field Visualization -- Constructing 3D Elliptical Gaussians for Irregular Data -- From Sphere Packing to the Theory of Optimal Lattice Sampling -- Reducing Interpolation Artifacts by Globally Fairing Contours -- Time- and Space-efficient Error Calculation for Multiresolution Direct Volume Rendering -- Massive Data Visualization: A Survey -- Compression and Occlusion Culling for Fast Isosurface Extraction from Massive Datasets -- Volume Visualization of Multiple Alignment of Large Genomic DNA -- Model-based Visualization - Computing Perceptually Optimal Visualizations En línea: http://dx.doi.org/10.1007/b106657 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34006 Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration [documento electrónico] / SpringerLink (Online service) ; Torsten Möller ; Bernd Hamann ; Robert D. Russell . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2009 . - X, 350 p. 183 illus., 134 illus. in color : online resource. - (Mathematics and Visualization, ISSN 1612-3786) . ISBN : 978-3-540-49926-8 Idioma : Inglés (eng) Palabras clave: Computer  science  Computers  Mathematics  graphics  Application  software  mathematics  Science  Applications  Theory  of  Computation  Computational  and  Numerical  Analysis  Graphics  Computing  Engineering Clasificación: 51 Matemáticas Resumen: Visualization is one of the most active and exciting areas of Mathematics and Computing Science, and indeed one which is only beginning to mature. Current visualization algorithms break down for very large data sets. While present approaches use multi-resolution ideas, future data sizes will not be handled that way. New algorithms based on sophisticated mathematical modeling techniques must be devised which will permit the extraction of high-level topological structures that can be visualized. For these reasons a workshop was organized at the Banff International Research Station, focused specifically on mathematical issues. A primary objective of the workshop was to gather together a diverse set of researchers in the mathematical areas relevant to the recent advances in order to discuss the research challenges facing this field in the next several years. The workshop was organized into five different thrusts: - Topology and Discrete Methods - Signal and Geometry Processing - Partial Differential Equations - Data Approximation Techniques - Massive Data Applications This book presents a summary of the research ideas presented at this workshop Nota de contenido: Maximizing Adaptivity in Hierarchical Topological Models Using Cancellation Trees -- The TOPORRERY: computation and presentation of multi-resolution topology -- Isocontour based Visualization of Time-varying Scalar Fields -- DeBruijn Counting for Visualization Algorithms -- Topological Methods for Visualizing Vortical Flows -- Stability and Computation of Medial Axes - a State-of-the-Art Report -- Local Geodesic Parametrization: an Ant’s Perspective -- Tensor-Fields Visualization Using a Fabric-like Texture Applied to Arbitrary Two-dimensional Surfaces -- Flow Visualization via Partial Differential Equations -- Iterative Twofold Line Integral Convolution for Texture-Based Vector Field Visualization -- Constructing 3D Elliptical Gaussians for Irregular Data -- From Sphere Packing to the Theory of Optimal Lattice Sampling -- Reducing Interpolation Artifacts by Globally Fairing Contours -- Time- and Space-efficient Error Calculation for Multiresolution Direct Volume Rendering -- Massive Data Visualization: A Survey -- Compression and Occlusion Culling for Fast Isosurface Extraction from Massive Datasets -- Volume Visualization of Multiple Alignment of Large Genomic DNA -- Model-based Visualization - Computing Perceptually Optimal Visualizations En línea: http://dx.doi.org/10.1007/b106657 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34006

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