Generation of unstructured meshes in 2-D, 3-D, and spherical geometries with embedded high-resolution sub-regions

Abstract

We present 2-D, 3-D, and spherical mesh generators for triangular and tetrahedral elements. The mesh nodes are treated as if they were linked by virtual springs that obey Hooke’s law. Given the desired lengths for the springs, a finite element problem is solved for optimal (static equilibrium) nodal positions. A ‘guide-mesh’ approach allows the user to define embedded high-resolution sub-regions within a coarser mesh. The method converges rapidly. For example, the algorithm is able to refine within a few iterations a specific region embedded in an unstructured tetrahedral spherical shell so that the edge-length factor l0r∕l0c=1∕33 where l0r and l0c are the desired spring length for elements inside the refined and coarse regions respectively. The algorithm also includes routines to locally improve the quality of the mesh and to avoid ill-shaped ‘sliver-like’ tetrahedra. We include a geodynamic modelling example as a direct application of the mesh generator.