Universal Meshes: Computing Tetrahedralization Conforming to Curved Surfaces

Three dimensional realistic simulation are often unsteady and include moving domains. One of major challenges associated with such simulations is the robust mesh generation for the moving domain. There has been significant research and development in this specific field[1, 2, 3, 4]. We describe a method for generating conforming tetrahedral mesh to the given C continuous surfaces in R immersed in a non-conforming tetrahedralization. The method consists of constructing a homeomorphic mapping from a subset of tetrahedrons in a background mesh to the ones conforming to the immersed set of surfaces. It relies on the way we parametrize the surfaces of the immersed domains over a collection of a nearby triangular faces with their closest point projections and extension of the same map for the local perturbations of the vertices in the neighborhood these surfaces.