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Universal Meshes: Computing Tetrahedralization Conforming to Curved Surfaces

Kabaria, Hardik and Adrian J. Lew

23rd International Meshing Roundtable, Elsevier Ltd., pp.Research Note, October 12-15 2014


23rd International Meshing Roundtable
London, UK
October 12-15,2014

Department of Mechanical Engineering, Stanford University, CA 94305 USA

Three dimensional realistic simulation are often unsteady and include mov- ing domains. One of major challenges associated with such simulations is the robust mesh generation for the moving domain. There has been significant re- search and development in this specific field[1, 2, 3, 4]. We describe a method for generating conforming tetrahedral mesh to the given C2 continuous sur- faces in R3 immersed in a non-conforming tetrahedralization. The method consists of constructing a homeomorphic mapping from a subset of tetrahe- drons 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.

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