High-Order Mesh Morphing for Boundary and Interface Fitting to Implicit Geometries. (May 2023)

• Record Type: Journal Article
• Authors: Barrera, Jorge-Luis; Kolev, Tzanio; Mittal, Ketan; Tomov, Vladimir
• Is Part Of: Computer aided design. Volume 158(2023)
• Publication Date: 2023-05
• Subjects: High-order -- Implicit meshing -- Mesh morphing -- r-adaptivity -- Finite elements -- TMOP; 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.2023.103499
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: We propose a method that morphs high-order meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero isocontour of a smooth discrete function. Common examples of this scenario include using level set functions to represent material interfaces in multimaterial configurations, and evolving geometries in shape and topology optimization. The proposed method formulates the mesh optimization problem as a variational minimization of the sum of a chosen mesh-quality metric using the Target-Matrix Optimization Paradigm (TMOP) and a penalty term that weakly forces the selected faces of the mesh to align with the target surface. The distinct features of the method are use of a source mesh to represent the level set function with sufficient accuracy, and adaptive strategies for setting the penalization weight and selecting the faces of the mesh to be fit to the target isocontour of the level set field. We demonstrate that the proposed method is robust for generating boundary- and interface-fitted meshes for curvilinear domains using different element types in 2D and 3D. Graphical abstract: Highlights: Implicit high-order meshing using boundary and interface fitting. Approach targets applications where the target surface is prescribed implicitly using level-set functions. r-adaptivity method is demonstrated to be robust at adapting easy-to-generate meshes to curvilinear boundaries and interfaces.