Grid Generation Methods
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Beschreibung
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.
Grid generation codes represent an indispensable tool for solving field prob lems in nearly all areas of applied mathematics. The use of these grid codes significantly enhances the productivity and reliability of the numerical analy sis of problems with complex geometry and complicated solutions. The science of grid generation is rather young and is still growing fast; new developments are continually occurring in the fields of grid methods, codes, and practical applications. Therefore there exists an evident need of students, researchers, and practitioners in applied mathematics for new books which coherently complement the existing ones with a description of new developments in grid methods, grid codes, and the concomitant areas of grid technology. The objective of this book is to give a clear, comprehensive, and easily learned description of all essential methods of grid generation technology for two major classes of grids: structured and unstructured. These classes rely on two somewhat opposite basic concepts. The basic concept of the former class is adherence to order and organization, while the latter is based on the absence of any restrictions. The present monograph discusses the current state of the art in methods of grid generation and describes new directions and new techniques aimed at the enhancement of the efficiency and productivity of the grid process. The emphasis is put on mathematical formulations, explanations, and examples of various aspects of grid generation.
Completely revised edition of this outstanding introduction into the most popular technologies for generating structured, unstructured and adaptive grids
Now with detailed description of monitor metrics in Beltrami and diffusion equations
Contains one of the most promising techniques of adaptive grid generation, based on the application of inverted Beltrami equations with respect to control metrics
Autor*in
Vladimir D. Liseikin
Themen in »Grid Generation Methods«
Adaptation Algebra Grid generation methods Grids computational physics differential equation mechanical engineering partial differential equation scientific computing transformation