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Harmonic parametrization of geodesic quadrangles on surfaces of constant curvature and 2-D quasi-isometric grids. (English) Zbl 0912.65126

This paper deals with a method for the generation of quasi-isometric boundary-fitted curvilinear coordinates for arbitrary domains. An approach on the basis of the quasi-isometric mappings theory and conformal representation of spherical and hyperbolic geometries is presented. The authors 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 robust. Illustrations of this techniques are presented for the case of one-element airfoil and several test domains.

MSC:

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
30C30 Schwarz-Christoffel-type mappings
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