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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.

519.63 --- 681.3*G18 --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Delay differential equations. --- Differential equations. --- Electronic books. -- local. --- Delay differential equations --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Calculus --- Applied Mathematics --- Numerical analysis --- Computer. Automation --- informatica --- numerieke analyse --- differentiaalvergelijkingen --- wiskunde --- Partial differential equations --- Mathematical Sciences --- Mathematics. --- Partial differential equations. --- Computer mathematics. --- Numerical analysis. --- Numerical Analysis. --- Computational Mathematics and Numerical Analysis. --- Partial Differential Equations. --- Mathematical analysis --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Science --- Delay equations (Differential equations) --- Delay functional differential equations --- Differential delay equations --- Differential equations --- Differential equations with lag --- Functional differential equations --- Retarded argument (Differential equations) --- Retarded differential equations --- Retarded functional differential equations --- Time-lag systems (Differential equations) --- Delay equations --- Retarded argument --- Time-lag equations --- 681.3 *G18 --- 517.91 Differential equations --- Computer science --- Differential equations, partial.

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Boundary value problems --- Numerical solutions. --- -519.6 --- 681.3*G17 --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Numerical solutions --- Computational mathematics. Numerical analysis. Computer programming --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 519.6 --- Boundary value problems - Numerical solutions.

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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.

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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.

Computer algorithms --Congresses. --- Computer graphics --Mathematical models --Congresses. --- Electronic data processing --Mathematical models --Congresses. --- Information visualization --Mathematical models --Congresses. --- Electronic data processing --- Computer algorithms --- Information visualization --- Computer graphics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Mathematics --- Mathematics - General --- Technology - General --- Sciences - General --- Computer Science --- Mathematical models --- Information visualization. --- Science --- Methodology. --- Scientific method --- Data visualization --- Visualization of information --- Computer science. --- Computers. --- Computer science --- Computer graphics. --- Application software. --- Computer mathematics. --- Computer Science. --- Computer Applications. --- Theory of Computation. --- Computational Mathematics and Numerical Analysis. --- Computer Graphics. --- Mathematics of Computing. --- Computational Science and Engineering. --- Mathematics. --- Logic, Symbolic and mathematical --- Information science --- Visual analytics --- Information theory. --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Engineering graphics --- Image processing --- Computer mathematics --- Discrete mathematics --- Communication theory --- Communication --- Cybernetics --- Informatics --- Digital techniques --- Computer science—Mathematics. --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Machine theory --- Calculators --- Cyberspace --- Application computer programs --- Application computer software --- Applications software --- Apps (Computer software) --- Computer software

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