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

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

Journal

Mathematics and Computers in Simulation
ISSN: 0378-4754

Output data

Year: 2008, Volume: 78, Number: 5-6, Pages: 575-592 Pages count : 8 DOI: 10.1016/j.matcom.2008.04.001

Tags

Riemmanian metric; Harmonic parametrization; Geodesic quadrangle; Quasi-isometric grid.

Authors

Chumakov Gennadii A. ¹

Affiliations

1	Sobolev Institute of Mathematics, Pr. Koptyuga 4, Novosibirsk 630090, Russia#TAB#

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 = 4 sin (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.

Chumakov G.A.
Riemmanian metric of harmonic parametrization of geodesic quadrangles and quasi-isometric grids
Mathematics and Computers in Simulation. 2008. V.78. N5-6. P.575-592. DOI: 10.1016/j.matcom.2008.04.001 WOS Scopus РИНЦ OpenAlex

Published online:

Apr 10, 2008

Web of science:	WOS:000258195100002
Scopus:	2-s2.0-46049120004
Elibrary:	13581104
OpenAlex:	W1979021078

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