3-D mesh generation for finite-element modelling of complex natural structures

The finite-element method is based on the discretization of a distributed system. The system subdivision process is called mesh generation. The number, order, geometric characteristics (shape, size and orientation) and physical characteristics (material properties, boundary conditions and load conditions) of elements in the mesh will affect the accuracy of the finite-element solution. The objective of this project is to establish a number of criteria for evaluating 3-D mesh-generation software, and to select the 3-D mesh generator that is most suitable for use in our software pipeline for modelling and simulation of complex natural structures. The evaluation criteria for this project include: ability to preserve the surface mesh during 3-D mesh generation; mesh quality; robustness; time efficiency; and cost. The mesh quality is assessed by visualization methods; histograms of the shape qualities and sizes of elements; solution residuals; condition numbers; and closeness to the exact solution as estimated by a convergence curve. Four unstructured mesh-generation programmes (GiD, Gmsh, GRUMMP and TetGen) have been evaluated. A thin block and three structures (one ligament and two ossicles) of the middle ear were chosen to be the models for the evaluation. A programme was developed to convert the surface definitions describing the models to the native file formats of the mesh-generation programmes, to verify that the surface meshes of these models could be successfully imported into the mesh-generation programmes, and to verify that the resulting volume meshes are topologically correct. The results of the evaluation indicate that the mean value of the shape qualities of elements, the root mean square of the solution residuals, and the closeness to the exact solution are good indicators of the overall mesh quality. The Gmsh programme is finally selected as the best 3-D mesh generator for the purposes of our software pipeline