Combining recursive spatial decompositions and domain Delaunay tetrahedrizations for meshing arbitrarily shaped curved solid models

Abstract

A recursive spatial decomposition (RSD) R( S) of a solid S is an approximation of 5 consisting of regular cells that either lie inside S (IN cells) or intersect the boundary of S (NIO cells). Automatic finite element meshing based on RSD has many advantages, compared to ‘global’ methods, particularly in the areas of adaptive meshing and parallel processing. However, transformation of the RSD R( S) into a finite element mesh requires the availability of a tetrahedrization method that (i) can handle arbitrarily shaped curved polyhedra (including objects with holes, non-manifolds, and disconnected objects), and (ii) produces tetrahedrizations of the IN and NIO cells that form a topologically valid mesh of the solid S. This paper introduces an RSD tetrahedrization procedure, based on the domain Delaunay tetrahedrization (DDT) method that satisfies the above requirements and also has an optimal average-case computational complexity. A complete description of the RSD/DDT mesh generation algorithm is presented along with a comparison with existing techniques as well as examples that demonstrate the robustness and efficiency of the method.