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Visualizing Mesh Adaptation Metric Tensors

Tchon, Ko-Foa, Julien Dompierre, Marie-Gabrielle Vallet and Ricardo Camarero

Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.353-364, September 19-22 2004

IMR
PROCEEDINGS

13th International Meshing Roundtable
Willimasburg, Virginia, USA
September 19-22, 2004

Ecole Polytechnique de Montreal
C.P. 6079, Succ. Centre-ville, Montreal (QC) H3C 3A7, Canada.
[ko-foa.tchon|julien.dompierre|marie-gabrielle.vallet|ricardo.camarero]@polymtl.ca

Abstract
Riemannian metric tensors are used to control the adaptation of meshes for finite element and finite volume computations. To study the numerous metric construction and manipulation techniques, a new method has been developed to visualize two-dimensional metrics without interference from any adaptation algorithm. This method traces a network of orthogonal tensor lines to form a pseudo-mesh visually close to a perfectly adapted mesh but without many of its constraints. Although the treatment of isotropic metrics could be improved, both analytical and solution-based metrics show the effectiveness and usefulness of the present method. Possible applications to adaptive quadrilateral and hexahedral mesh generation are also discussed.

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