Orthogonal Coordinate Meshes with Manageable Jacobian,

Abstract

Recent the problem of numerical generating curvilinear coordinate meshes has received a vast exploration because of its outstanding importance in solving the partial differential equations of continuous mechanics. The major advantage of this method is that the boundary of the region becomes a coordinate line which decidedly simplifies the numerical schemes for approximate integration of boundary value problems. In some since the method of adapted coordinates is an alternative to the method of finite elements. In two dimension the most natural way to create curvilinear meshes was, perhaps, the inversion of conformal mapping. This approach was generalized by means of variational principle. The coordinates obtained in this way, however, were not orthogonal in general and the Jacobian assumed in some cases incomfortable values approaching zero or infinity. It was due to the rigid prescription of the boundary points. The orthogonality has been restored only after reducing the conditions on the boundary points to the natural ones for a conformal mapping. In present note an other approach ensuring the Jacobian to be a priory prescribed function is attempted. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1982
Accession Number
ADP001009

Entities

People

  • C. I. Christov

Organizations

  • Bulgarian Academy of Sciences

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Cartography
  • Conformal Mapping
  • Coordinate Systems
  • Demographic Cohorts
  • Differential Equations
  • Equations
  • Grids
  • Partial Differential Equations
  • Variational Principles

Readers

  • Educational Psychology
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)