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Riemmanian metric of harmonic parametrization of geodesic quadrangles and quasi-isometric grids

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  • Chumakov, Gennadii A.

Abstract

We consider the problem of generating a 2D structured boundary-fitting rectangular grid in a curvilinear quadrangle D with angles αi=ϕi+π/2, where −π/2<ϕi<π/2, i=1,…,4. We construct a quasi-isometric mapping of the unit square onto D; it is proven to be the unique solution to a special boundary-value problem for the Beltrami equations. We use the concept of “canonical domains”, i.e., the geodesic quadrangles with the angles α1,…,α4 on surfaces of constant curvature K=4sin⁡(ϕ1+ϕ2+ϕ3+ϕ4)/2, to introduce a special class of coefficients in the Beltrami equations with some attractive invariant properties. In this work we obtain the simplest formula representation of coefficients gjk, via a conformally equivalent Riemannian metric of harmonic parametrization of geodesic quadrangles. We also propose a new, more robust method to compute the metric for all parameter values.

Suggested Citation

  • Chumakov, Gennadii A., 2008. "Riemmanian metric of harmonic parametrization of geodesic quadrangles and quasi-isometric grids," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(5), pages 575-592.
    • Handle: RePEc:eee:matcom:v:78:y:2008:i:5:p:575-592
    DOI: 10.1016/j.matcom.2008.04.001
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