Combining High-Order Metric Interpolation and Geometry Implicitization for Curved r-Adaption. (April 2023)

• Record Type: Journal Article
• Authors: Aparicio-Estrems, Guillermo; Gargallo-Peiró, Abel; Roca, Xevi
• Is Part Of: Computer aided design. Volume 157(2023)
• Publication Date: 2023-04
• Subjects: r-adaption -- Mesh optimization -- Curved high-order meshes; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2023.103478
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: We detail how to use Newton's method for distortion-based curved r -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) r -adaption. This capability will be critical in global and cavity-based curved (straight-edged) high-order mesh adaption. Graphical abstract: Highlights: Second-order optimization for simultaneous curved r-adaption to metric and geometry. Objective function accounting for metric and geometry deviations. Implicit model representation for 2D and 3D NURBS models. First- and second-order derivatives of the implicit representation of the model. First- and second-order derivatives of a log-Euclidean high-order metric interpolation.