Towards tetrahedral meshing with decoupled element and boundary constraints

In tetrahedral mesh generation, the constraints imposed by adaptive element size, good tetrahedral quality (shape measured by some local metric), and material boundaries are often in conflict. Attempts to satisfy these conditions simultaneously frustrate many conventional approaches. We propose a new strategy for boundary conforming meshing that decouples the problem of building tetrahedra of proper size and shape from the problem of conforming to geometric boundaries. The proposed strategy is to first build a background mesh with the appropriate tetrahedral properties, and then to use a stenciling method to divide or cleave these elements to get a set of conforming tetrahedra, while strictly limiting the impacts cleaving has on element shape. Our contributions includes a new method for building graded, unstructured meshes and a generalization of the isosurface stuffing and lattice cleaving algorithms to unstructured background meshes.