Electronic Journal of Differential Equations,
Conference 01 (1998), pp. 55-79. 

Title: Harmonic parameterization of geodesic quadrangles on surfaces of constant Curvature  and 2-D Quasi-Isometric Grids 


Authors: Gennadii A. Chumakov (Sobolev Institute of Math. Novosibirsk, Russia)
         Sergei G. Chumakov (Univ. of Wisconsin, Madison, WI, USA) 
 
Abstract: 
A method for the generation of quasi-isometric boundary-fitted
  curvilinear coordinates for arbitrary domains is developed on the
  basis of the quasi-isometric mappings theory and conformal
  representation of spherical and hyperbolic geometries.  A
  one-parameter family of Riemannian metrics with some attractive
  invariant properties is analytically described.  We construct the
  quasi-isometric mapping between the regular computation domain $\cal
  R$ and a given physical domain $\cal D$ that is conformal with
  respect to the unique metric from the proposed one-parameter class.
  The identification process of the unknown parameter takes into
  account the high parametric sensitivity of metrics to the parameter.
  For this purpose we use a new technique for finding the geodesic
  quadrangle with given angles and a conformal module on the surface
  of constant curvature, which makes the method more robust.  The
  method allows more direct control of the grid cells size and angle
  over the field as the grid is refined.  Illustrations of this
  technique are presented for the case of one-element airfoil and
  several test domains.


Published November 12, 1998.
Math Subject Classifications: 65N50, 30C30.
Key Words: regular grid generation; quasi-isometric mappings; geodesic grids; geodesic quadrangles; surfaces of constant curvature.