On the invertibility of mappings arising
in 2D grid generation problems |
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Authors: | P Clément R Hagmeijer G Sweers |
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Institution: | (1) Department of Pure Mathematics, Delft University of Technology, PObox 5031, NL-2600 GA Delft, The Netherlands; e-mail: clement@twi.tudelft.nl , NL;(2) Department of Theoretical Aerodynamics, National Aerospace Laboratory N.L.R., POBox 90502 NL-1006 BM Amsterdam, The Netherlands , NL;(3) Department of Pure Mathematics, Delft University of Technology, PObox 5031, NL-2600 GA Delft, The Netherlands; e-mail: sweers@twi.tudelft.nl , NL |
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Abstract: | Summary.
In adapting a grid for a Computational Fluid Dynamics problem one uses a
mapping from 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 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.
Received
March 1, 1994 / Revised version received March 8, 1995 |
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Keywords: | Mathematics Subject Classification (1991): 35J25 65M50 76B05 |
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