Invertibility of Mappings Arising in 2D Grid Generation Problems

摘要

In adapting a grid for a Computational Fluid Dynamics problem one uses a mappingfrom the unit square onto itself that is the solution of an elliptic partial differential equation with rapidly varying coefficients. For a regular discretization this mapping has to be invertible. We will show that such a result holds for general elliptic operators (in two dimensions). The Carleman-Hartman-Wintner Theorem will be fundamental in our proof. We will also explain why such a general result cannot be expected to hold for the (three-dimensional) cube. (Copyright (c) 1994 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)