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Defining Quality Measures for High-Order Planar Triangles and Curved Mesh Generation

Roca, Xevi, Abel Gargallo-Peiro and Josep Sarrate

20th International Meshing Roundtable, Springer-Verlag, pp.365-383, October 23-26 2011


20th International Meshing Roundtable
Paris, France
October 23-26, 2011

Laboratori de Calcul Numeric (LaCaN), Universitat Politecnica de Catalunya, Barcelona 08034, Spain, Department of Aeronautics and Astronautics Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Email: fxevi.roca,abel.gargallo,,

We present a technique to extend any Jacobian based quality measure for linear elements to high-order isoparametric planar triangles of any interpolation degree. The extended quality measure is obtained as the inverse of the distortion of the high-order element with respect to an ideal element. To measure the high- order distortion, we integrate on the curved element the inverse of the Jacobian based quality measure. Thus, we can proof that if the Jacobian based quality is invariant under a particular ane mapping, then the resulting quality measure is also invariant under that mapping. In addition, we check that the quality measure detects non-valid and low-quality high-order elements. Finally, we present and test an approach to generate curved meshes by minimizing the high-order distortion measure of the elements.

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