  Centroidal Voronoi tessellation (CVT)-based mesh generation is a very
effective technique for creating high-quality Voronoi meshes and their dual
Delaunay triangulations that often play a crucial role in applications,
including ocean and atmospheric simulations using finite volume schemes. In the
next generation climate models, the spacing scales change dramatically across
the whole sphere and require ultra-high resolution and smooth transitions from
coarse to fine grid regions. Thus fast and robust spherical CVT (SCVT) meshing
algorithms become highly desirable. In this paper, we first propose a
Lloyd-preconditioned limited-memory BFGS method for constructing SCVTs that is
also applicable to the construction of CVTs of general domains. This method is
then parallelized based on overlapping domain decomposition, enabling excellent
scalability on distributed systems. Results of several computational
experiments show that the new method could incur computational time costs one
order of magnitude smaller compared with some existing methods for generating
large-scale highly variable-resolution meshes, while also providing
significantly improvements in mesh quality.
