An Algorithm for Three-Dimensional Mesh Generation for Arbitrary Regions with Cracks

An algorithm for generating unstructured tetrahedral meshes of arbitrarily shaped three-dimensional regions is described. The algorithm works for regions without cracks, as well as for regions with one or multiple cracks. The algorithm incorporates aspects of well known meshing procedures, but includes some original steps. It uses an advancing front technique, along with an octree to develop local guidelines for the size of generated elements. The advancing front technique is based on a standard procedure found in the literature, with two additional steps to ensure valid volume mesh generation for virtually any domain. The first additional step is related to the generation of elements only considering the topology of the current front, and the second additional step is a back-tracking procedure with face deletion, to ensure that a mesh can be generated even when problems happen during the advance of the front. To improve mesh quality (as far as element shape is concerned), an a posteriori local mesh improvement procedure is used. The performance of the algorithm is evaluated by application to a number of realistically complex, cracked geometries.