3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral Meshing

Abstract

We present a method for the generation of higher-order tetrahedral meshes. In contrast to previous methods, the curved tetrahedral elements are guaranteed to be free of degeneracies and inversions while conforming exactly to prescribed piecewise polynomial surfaces, such as domain boundaries or material interfaces. Arbitrary polynomial order is supported. Algorithmically, the polynomial input surfaces are first covered by a single layer of carefully constructed curved elements using a recursive refinement procedure that provably avoids degeneracies and inversions. These tetrahedral elements are designed such that the remaining space is bounded piecewise linearly. In this way, our method effectively reduces the curved meshing problem to the classical problem of linear mesh generation (for the remaining space).