Combining high-order metric interpolation and geometry implicitization for curved $r$-adaption
| Autor: | Guillermo Aparicio-Estrems, Abel Gargallo-Peiró, Xevi Roca |
|---|---|
| Přispěvatelé: | Barcelona Supercomputing Center |
| Rok vydání: | 2023 |
| Předmět: |
Informàtica::Aplicacions de la informàtica::Aplicacions informàtiques a la física i l‘enginyeria [Àrees temàtiques de la UPC]
Mesh Mesh optimization Computational Engineering Finance and Science (cs.CE) FOS: Computer and information sciences r-adaption Simulació per ordinador Curved high-order meshes Computer Science - Computational Engineering Finance and Science Computer Graphics and Computer-Aided Design Industrial and Manufacturing Engineering Computer Science Applications |
| DOI: | 10.48550/arxiv.2303.11979 |
| Popis: | We detail how to use Newton’s method for distortion-based curved -adaption to a discrete high-order metric field while matching a target geometry. Specifically, we combine two terms: a distortion measuring the deviation from the target metric; and a penalty term measuring the deviation from the target boundary. For this combination, we consider four ingredients. First, to represent the metric field, we detail a log-Euclidean high-order metric interpolation on a curved (straight-edged) mesh. Second, for this metric interpolation, we detail the first and second derivatives in physical coordinates. Third, to represent the domain boundaries, we propose an implicit representation for 2D and 3D NURBS models. Fourth, for this implicit representation, we obtain the first and second derivatives. The derivatives of the metric interpolation and the implicit representation allow minimizing the objective function with Newton’s method. For this second-order minimization, the resulting meshes simultaneously match the curved features of the target metric and boundary. Matching the metric and the geometry using second-order optimization is an unprecedented capability in curved (straight-edged) -adaption. This capability will be critical in global and cavity-based curved (straight-edged) high-order mesh adaption. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 715546. This work has also received funding from the Generalitat de Catalunya under grant number 2017 SGR 1731. The work of X. Roca has been partially supported by the Spanish Ministerio de Econom´ıa y Competitividad under the personal grant agreement RYC-2015-01633. |
| Databáze: | OpenAIRE |
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