Delaunay tetrahedralization in a 3-D free-lagrangian multimaterial code

Abstract

A Delaunay tetrahedralization technique for tesselating space, without any multimaterial tetrahedra for a given mass-point distribution, in a three-dimensional, multimaterial, free-Lagrangian code is described. The approach involves first connecting only the points that do not result in degeneracies, and adding the degenerate points later on, so that the degeneracies affect the mesh only locally. First, the entire Delaunay tetrahedral mesh is generated disregrading multiple materials. The multimaterial tetrahedral connections are then broken by adding new points at the multimaterial connections. The technique inherently involves O(n ²) arithmetic operations, where n is the number of mass points; however, we have reduced it to O[nlog(n)] operations by utilizing a “binning” approach. The algorithm is fully vectorized on the Cray family of supercomputers