Abstract: A method for generating and refining meshes for a three-dimensional domain. The method includes generating a initial Delaunay mesh; identifying selection balls whose radius-edge ratio is greater than an upper bound value; and refining the generated Delaunay mesh by inserting points within the selection balls to reduce the radius-edge ratios of all tetrahedral in the mesh below a given upper bound value. Selection balls include one-dimensional selection balls, two-dimensional selection balls, and three-dimensional selection balls. The selection balls of a lower dimension are refined before the selection balls of a higher dimension are refined.

Abstract: A method for generating mesh from an image. The method includes inputting an image; setting a quality bound and a fidelity bound for a mesh to be generated; generating an initial mesh for the image with a maximum fidelity and a very high quality; generating a refined mesh by coarsening the initial mesh while maintaining the quality bound and the fidelity bound. The refined mesh includes a smaller number of elements than that of the initial mesh.

Abstract: A method of mesh generation processing for a bounded domain is provided. The bounded domain is divided into constituent sub-domains with a portion of the sub-domains being assigned to each of a plurality of processors. The processors are operated independently and in parallel. Each processor (i) discretizes the closed boundary for each of its sub-domains to generate coordinates that are identical for each portion of adjoining sub-domain boundaries and that satisfy specific conditions that optimize a selected mesh generation technique, and (ii) generates a mesh for each sub-domain assigned thereto using corresponding ones of the coordinates and the selected mesh generation technique.