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A Computational Differential Geometry Approach to Grid Generation

  • Book
  • © 2004

Overview

Authors:
  1. Vladimir D. Liseikin

    1. Institute of Computational Technologies, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 90, Russia

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  • Geometric methods in grid generation is a fairly recent subject with many applications in scientific computing
  • So far the literature on the subject is sparse
  • Includes supplementary material: sn.pub/extras

Part of the book series: Scientific Computation (SCIENTCOMP)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XIV
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  2. Geometric Background to Grid Technology

    1. Front Matter

      Pages 1-3
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    2. Introductory Notions

      • Vladimir D. Liseikin
      Pages 5-32

    3. General Coordinate Systems in Domains

      • Vladimir D. Liseikin
      Pages 33-51

    4. Geometry of Curves

      • Vladimir D. Liseikin
      Pages 53-58

    5. Multidimensional Geometry

      • Vladimir D. Liseikin
      Pages 59-106

  3. Application to Advanced Grid Technology

    1. Front Matter

      Pages 107-110
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    2. Comprehensive Grid Models

      • Vladimir D. Liseikin
      Pages 111-136

    3. Relations to Monitor Manifolds

      • Vladimir D. Liseikin
      Pages 137-168

    4. Grid Equations with Respect to Intermediate Transformations

      • Vladimir D. Liseikin
      Pages 169-194

    5. Control of Grid Clustering

      • Vladimir D. Liseikin
      Pages 195-240

    6. Numerical Implementation of Grid Generator

      • Vladimir D. Liseikin
      Pages 241-254

  4. Back Matter

    Pages 255-264
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Keywords

About this book

Grid technology whose achievements have significant impact on the efficiency of numerical codes still remains a rapidly advancing field of computational and applied mathematics. New achievements are being added by the creation of more sophisticated techniques, modification of the available methods, and implementation of more subtle tools as well as the results of the theories of differential equations, calculas of variations, and Riemannian geometry being applied to the formulation of grid models and analysis of grid properties. The development of comprehensive differential and variational grid gen­ eration techniques reviewed in the monographs of J. F. Thompson, Z. U. A. Warsi, C. W. Mastin, P. Knupp, S. Steinberg, V. D. Liseikin has been largely based on a popular concept in accordance with which a grid model realizing the required grid properties should be formulated through a linear combina­ tion of basic and control grid operators with weights. A typical basic grid operator is the operator responsible for the well-posedness of the grid model and construction of unfolding grids, e. g. the Laplace equations (generalized Laplace equations for surfaces) or the functional of grid smoothness which produces fixed nonfolding grids while grid clustering is controlled by source terms in differential grid formulations or by an adaptation functional in vari­ ational models. However, such a formulation does not obey the fundamental invariance laws with respect to parameterizations of physical geometries. It frequently results in cumbersome governing grid equations whose choice of weight and control functions provide conflicting grid requirements.

Authors and Affiliations

  • Institute of Computational Technologies, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 90, Russia

    Vladimir D. Liseikin

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