Mathematical Aspects of Numerical Grid Generation: Frontiers in Applied Mathematics, No 8
The mathematical aspects of grid generation are discussed to provide a deeper understanding of the algorithms and their limitations.
Format: Paperback, English, 157 pages
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"Numerical grid generation frequently plays a central role in complex numerical modeling problems. Strangely, essentially none of the important methods have been analyzed mathematically. This volume is an excellent start in correcting that situation." -Stanly L. Steinberg (1-NM-S), Mathematical Reviews, Issue 92h.
Numerical grid generation plays a critical role in any scientific computing problem when the geometry of the underlying region is complex or when the solution has a complex structure. The mathematical aspects of grid generation are discussed to provide a deeper understanding of the algorithms and their limitations. Variational methods are emphasized because they are more robust, but elliptic and transcendental algebraic methods are also considered.
Computational engineers and scientists, particularly those interested in large scale scientific computing, are the audience for this book. Many open problems are discussed, so the volume will also be of interest to applied mathematicians and numerical analysts. The book is self-contained; however, references are provided for any required background if needed. Jose E. Castillo is director of the Interdisciplinary Research Center and associate professor in the department of mathematics at San Diego State University. He has authored various publications and has developed grid-generation algorithms based on intuitive discrete geometric notions.
Table of Contents
|1||Introduction, J. E. Castillo and S. Steinberg|
|2||Elliptic Grid Generation and Conformal Mapping, C. W. Mastin|
|3||Continuum Variational Formulation, J. E. Castillo|
|4||Discrete Variational Grid Generation, J. E. Castillo|
|5||Bifurcation of Grids on Curves, S. Steinberg and P. J. Roache|
|6||Intrinsic Algebraic Grid Generation, P. M. Knupp|
|7||Surface Grid Generation and Differential Geometry, Z. U. A. Warsi|
|8||Harmonic Maps in Grid Generation, A. Dvinsky|
|9||On Harmonic Maps, G. Liao|
|10||Mathematical Aspects of Harmonic Grid Generation, S. S. Sritharan|