Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
On the provably tight approximation of optimal meshing for non-convex regions
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
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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.