Novosibirsk, Russia, May, 30 – June, 4, 2011

"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

## Чумаков Г.А. Чумаков С.Г.## Canonical domains for almost orthogonal quasi-isometric grids## Reporter: Чумаков Г.А.
A special class of canonical domains is discussed for the generation of quasi-isometric grids. The base computational strategy of our approach is that the physical domain is decomposed into five non-overlapping blocks, which are automatically generated by solving a variational problem. Four of these blocks - the ones that contain the corners - are conformally equivalent to geodesic quadrangles on surfaces of constant curvature, while the fifth block is a conformal image of a non-convex polygon composed of five planar rectangles (or a large rectangle with four small rectangles cut out of its corners). To ensure that the angles of the physical and canonical domains coincide and the conformal modules are the same, the four corner blocks are taken to be geodesic quadrangles on surfaces of constant curvature, namely, spherical, planar or Lobachevsky plane, depending on the angles of the physical domain. Within each of these blocks a quasi-isometric grid is generated. Orthogonality of coordinate lines holds in the fifth, central block.
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