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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


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.

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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