Fast High-Order Mesh Correction for Metric-Based Cavity Remeshing and a Posteriori Curving of [formula omitted] Tetrahedral Meshes

Abstract

A new high-order mesh correction method is introduced. Using the simplex algorithm, it maximizes directly the minimum of all control coefficients depending on a control point. This method provides the global optimum as quickly as to evaluate the min 8 times on average. The basic principle is applicable to all common element types (tetrahedra, hexahedra pyramids, prisms) and degrees. Meshes are corrected globally using this simplex-based Jacobian corrector in iterative smoothing.Riemannian edge length minimization is presented for metric-based high-order mesh curving. It is consistent with log-Euclidean metric interpolation, which is extended to high-order meshes. The interpolated metric field is differentiated analytically, with applications to other geometric quantities (quality, Jacobian conformity). Edge length minimization is fast and flexible as it can be used with metrics deriving from adaptation or e.g. propagated surface metrics.The cavity operator is a general topological operator that can apply insertions, collapses and generalized swaps. It is extended to P2 meshes through a modular approach with curvature applied in two steps. Prescribed curvature is the result of CAD/P3 surrogate projection on the boundary and of metric-based curvature in the interior. Necessary curvature results from simplex-based correction of the curved cavity. Both curvature schemes can easily be replaced by alternatives.Several 3D numerical results on difficult academic and realistic CFD test-cases are presented. P2 tetrahedral meshes with up to 20M tetrahedra are corrected with curved boundary in between 10 s and 3 m30 s depending on target minimum Jacobian determinant.