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We present 2-D, 3-D, and spherical mesh generators for the Finite ElementMethod (FEM) using triangular and tetrahedral elements. The mesh nodes aretreated as if they were linked by virtual springs that obey Hooke's law. Giventhe desired length for the springs, the FEM is used to solve for the optimalnodal positions for the static equilibrium of this spring system. A'guide-mesh' approach allows the user to create embedded high resolutionsub-regions within a coarser mesh. The method converges rapidly. For example,in 3-D, the algorithm is able to refine a specific region within anunstructured tetrahedral spherical shell so that the edge-length factor$l_{0r}/l_{0c} = 1/33$ within a few iterations, where $l_{0r}$ and $l_{0c}$ arethe desired spring length for elements inside the refined and coarse regionsrespectively. One use for this type of mesh is to model regional problems as afine region within a global mesh that has no fictitious boundaries, at only asmall additional computational cost. The algorithm also includes routines tolocally improve the quality of the mesh and to avoid badly shaped'slivers-like' tetrahedra.

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