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Defining metric-aware size-shape measures to validate and optimize curved high-order meshes
- Source :
- Computer-Aided Design, Volume 168, March 2024, 103667
- Publication Year :
- 2024
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Abstract
- We define a regularized size-shape distortion (quality) measure for curved high-order elements on a Riemannian space. To this end, we measure the deviation of a given element, straight-sided or curved, from the stretching, alignment, and sizing determined by a target metric. The defined distortion (quality) is suitable to check the validity and the quality of straight-sided and curved elements on Riemannian spaces determined by constant and point-wise varying metrics. The examples illustrate that the distortion can be minimized to curve (deform) the elements of a given high-order (linear) mesh and try to match with curved (linear) elements the point-wise stretching, alignment, and sizing of a discrete target metric tensor. In addition, the resulting meshes simultaneously match the curved features of the target metric and boundary. Finally, to verify if the minimization of the metric-aware size-shape distortion leads to meshes approximating the target metric, we compute the Riemannian measures for the element edges, faces, and cells. The results show that, when compared to anisotropic straight-sided meshes, the Riemannian measures of the curved high-order mesh entities are closer to unit. Furthermore, the optimized meshes illustrate the potential of curved $r$-adaptation to improve the accuracy of a function representation.<br />Comment: 49 pages, 23 figures
- Subjects :
- Computer Science - Computational Engineering, Finance, and Science
Subjects
Details
- Database :
- arXiv
- Journal :
- Computer-Aided Design, Volume 168, March 2024, 103667
- Publication Type :
- Report
- Accession number :
- edsarx.2403.13528
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.cad.2023.103667