Abstract
We propose a new algorithm for the generation of orthogonal grids on regions bounded by arbitrary number of polynomial inequalities. Instead of calculation of the grid nodes positions for a particular region, we perform all calculations for general polynomials given with indeterminate coefficients. The first advantage of this approach is that the calculations can be performed only once and then used to generate grids on arbitrary regions and of arbitrary mesh size with constant computational costs. The second advantage of our algorithm is the avoidance of singularities, which occur while using the existing algebraic grid generation methods and lead to the intersection of grid lines. All symbolic calculation can be performed with general purpose Computer Algebra Systems, and expressions obtained in this way can be translated in Java/C++ code.
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Chibisov, D., Ganzha, V., Mayr, E.W., Vorozhtsov, E.V. (2005). Generation of Orthogonal Grids on Curvilinear Trimmed Regions in Constant Time. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2005. Lecture Notes in Computer Science, vol 3718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11555964_9
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DOI: https://doi.org/10.1007/11555964_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28966-1
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