P2 Mesh Optimization Operators

Abstract

Curved mesh generation starting from a P 1 mesh relies on mesh deformation and mesh optimization techniques. Mesh optimization techniques consist in locally modifying the mesh in order to improve it with respect to a given quality criterion. This work presents the generalization of two mesh quality-based optimization operators to P 2 meshes. The generalized operators consist in mesh smoothing and generalized swapping. With the use of these operators, P 2 mesh generation starting from a P 1 mesh is more robust and P 2 connectivity-change moving mesh methods for large displacements are now possible.

Combining High-Order Metric Interpolation and Geometry Implicitization for Curved r-Adaption

“…However, to properly match the requirements of high-order methods in h-adaption, it is mandatory to use local cavity operators for curved meshes. Regarding these curved operators, we have planned to combine existing approaches [14,16,25,52] with our approaches. Specifically, our distortion minimization for high-order metric and curved boundaries can also optimize a local cavity.…”

Local element operations for curved simplex meshes

“…There is practically no literature on the use of local element operations for curved meshes. To the best of the authors' knowledge, the only existing work on high‐order mesh operations 29 considers face and edge swaps for tetrahedral meshes with second‐order ($$$ {P}^2 $$$) elements.…”