Two-dimensional metric tensor visualization using pseudo-meshes
| Autor: | Marie-Gabrielle Vallet, Julien Dompierre, Ricardo Camarero, François Guibault, Ko-Foa Tchon |
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| Rok vydání: | 2006 |
| Předmět: |
Quadrilateral
Finite volume method General Engineering Topology Finite element method Computer Science Applications Computer Science::Graphics Mesh generation Modeling and Simulation Polygon mesh Tensor Software Eigenvalues and eigenvectors Smoothing ComputingMethodologies_COMPUTERGRAPHICS Mathematics |
| Zdroj: | Engineering with Computers. 22:121-131 |
| ISSN: | 1435-5663 0177-0667 |
| DOI: | 10.1007/s00366-006-0012-3 |
| Popis: | 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 an adaptation algorithm. This method traces a network of orthogonal tensor lines, tangent to the eigenvectors of the metric field, to form a pseudo-mesh visually close to a perfectly adapted mesh but without many of its constraints. Anisotropic metrics can be visualized directly using such pseudo-meshes but, for isotropic metrics, the eigensystem is degenerate and an anisotropic perturbation has to be used. This perturbation merely preserves directional information usually present during metric construction and is small enough, about 1% of the prescribed target element size, to be visually imperceptible. Both analytical and solution-based examples show the effectiveness and usefulness of the present method. As an example, pseudo-meshes are used to visualize the effect on metrics of Laplacian-like smoothing and gradation control techniques. Application to adaptive quadrilateral mesh generation is also discussed. |
| Databáze: | OpenAIRE |
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