3D volumetric isotopological meshing for finite element and isogeometric based reduced order modeling

This paper presents a generic framework to construct 3D structured volumetric meshes of complicated geometry and arbitrary topology. Structured meshes are well-suited for reduced order model applications with geometric parameters. For that purpose, we use the triangulated solid 3D model’s boundary provided from B-Rep CAD (Boundary-Representation in Computer Aided Design) models. The input triangulated mesh is decomposed into a set of cuboids in two steps: pants decomposition and cuboid decomposition. Both segmentations understand the geometry and features of meshes. Cuboid decomposition splits a surface into a set of quadrilateral patches which can define a volumetric layout of the associated boundary surface. Using aligned global parameterization, patches of the cuboid decomposition are re-positioned on the surface in a way to achieve low overall distortion, and alignment to principal curvature directions and sharp features. The optimization process is thought to design cross fields with topological and geometrical constraints. Using the optimized cuboid decomposition, a volumetric layout is extracted. Based on the global parameterization and the structured volumetric layout previously computed, a 3D volumetric parameterization is deducted. For different geometrical instances with the same topology but different geometries, the proposed method allows to have the same representation: 3D volumetric isotopological meshes holding the same connectivity. MEG-IsoHex method is introduced to compare fields on 3D hexahedral meshes. The efficiency and the robustness of the proposed approach are illustrated through a remeshing case for large deformations and reduced order models using isogeometric analysis.