Fast Spherical Centroidal Voronoi Mesh Generation: A Lloyd-preconditioned LBFGS Method in Parallel

TL;DR

This paper introduces a fast, parallel Lloyd-preconditioned LBFGS algorithm for spherical centroidal Voronoi tessellations, significantly improving speed and quality for high-resolution climate modeling meshes.

Contribution

It presents a novel Lloyd-preconditioned LBFGS method for spherical CVT generation, with parallelization for scalable large-scale mesh creation.

Findings

Achieves an order of magnitude reduction in computational time.

Provides high-quality meshes with smooth resolution transitions.

Demonstrates scalability on distributed systems.

Abstract

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.