Tensors and Differential Geometry Applied to Analytic and Numerical Coordinate Generation

Abstract

The two main objectives of this monograph are, (1) to present and collect at one place some important classical results and concepts from the theories of tensor analysis and differential geometry, and (2) to use the presented results in devising differential models for generating coordinates in arbitrarily bounded regions. Though most of the discussions on tensors and differential geometry are in the context of curvilinear coordinate generation, the first two parts can profitably be used for applied problems in various branches of engineering both by students and researchers. The last part of the monograph is concerned with the development of two methods, based on differential equations, for the generation of coordinates. The selected models are based on elloptic partial differential equations which can be solved on a computer to provide smooth differentiable coordinate curves in the region of interest.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1981
Accession Number
ADA096419

Entities

People

  • Z. U. Warsi

Organizations

  • Mississippi State University

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Computational Fluid Dynamics
  • Computational Science
  • Coordinate Systems
  • Differential Equations
  • Differential Geometry
  • General Relativity
  • Geometric Forms
  • Geometry
  • Industrial Research
  • Lines (Geometry)
  • Materials
  • Partial Differential Equations
  • Relativity Theory
  • Special Relativity
  • Theorems
  • Three Dimensional
  • Two Dimensional

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Systems Analysis and Design