Visualizing Mesh Adaptation Metric Tensors

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.