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This book is an introduction to structured and unstructured grid methods in scientific computing, addressing graduate students, scientists as well as practitioners. Basic local and integral grid quality measures are formulated and new approaches to mesh generation are reviewed. In addition to the content of the successful first edition, a more detailed and practice oriented description of monitor metrics in Beltrami and diffusion equations is given for generating adaptive numerical grids. Also, new techniques developed by the author are presented, in particular a technique based on the inverted form of Beltrami's partial differential equations with respect to control metrics. This technique allows the generation of adaptive grids for a wide variety of computational physics problems, including grid clustering to given function values and gradients, grid alignment with given vector fields, and combinations thereof. Applications of geometric methods to the analysis of numerical grid behavior as well as grid generation based on the minimization of functionals of smoothness, conformality, orthogonality, energy, and alignment complete the second edition of this outstanding compendium on grid generation methods.

Mathematics --- Mathematical physics --- Applied physical engineering --- Engineering sciences. Technology --- Computer science --- Computer. Automation --- ICT (informatie- en communicatietechnieken) --- toegepaste wiskunde --- theoretische fysica --- computers --- economie --- informatica --- externe fixatie (geneeskunde --- wiskunde --- ingenieurswetenschappen --- fysica --- Computer graphics. --- Infographie --- Grilles (analyse numérique) --- Numerical grid generation --- Grilles (analyse numérique) --- Numerical grid generation (Numerical analysis)

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This new edition provides a description of current developments relating to grid methods, grid codes, and their applications to actual problems. Grid generation methods are indispensable for the numerical solution of differential equations. Adaptive grid-mapping techniques, in particular, are the main focus and represent a promising tool to deal with systems with singularities. This 3rd edition includes three new chapters on numerical implementations (10), control of grid properties (11), and applications to mechanical, fluid, and plasma related problems (13). Also the other chapters have been updated including new topics, such as curvatures of discrete surfaces (3). Concise descriptions of hybrid mesh generation, drag and sweeping methods, parallel algorithms for mesh generation have been included too. This new edition addresses a broad range of readers: students, researchers, and practitioners in applied mathematics, mechanics, engineering, physics and other areas of applications.

Mathematics --- Physics --- Applied physical engineering --- Engineering sciences. Technology --- Computer science --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- ICT (informatie- en communicatietechnieken) --- computers --- economie --- informatica --- simulaties --- wiskunde --- informaticaonderzoek --- KI (kunstmatige intelligentie) --- ingenieurswetenschappen --- fysica --- computerkunde --- AI (artificiële intelligentie)

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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. This monograph gives a detailed treatment of applications of geometric methods to advanced grid technology. It focuses on and describes a comprehensive approach 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. In this second edition the author takes a more detailed and practice-oriented approach towards explaining how to implement the method by: Employing geometric and numerical analyses of monitor metrics as the basis for developing efficient tools for controlling grid properties. Describing new grid generation codes based on finite differences for generating both structured and unstructured surface and domain grids. Providing examples of applications of the codes to the generation of adaptive, field-aligned, and balanced grids, to the solutions of CFD and magnetized plasmas problems. The book addresses both scientists and practitioners in applied mathematics and numerical solution of field problems.

Differential geometry. Global analysis --- Numerical analysis --- Mathematics --- Mathematical physics --- Classical mechanics. Field theory --- Thermodynamics --- Computer. Automation --- thermodynamica --- differentiaal geometrie --- informatica --- wiskunde --- algoritmen --- fysica --- mechanica --- numerieke analyse