A Parallel Variational Mesh Quality Improvement Method for Tetrahedral Meshes Based on the MMPDE Method

There are numerous large-scale applications requiring mesh adaptivity, e.g., cardiac electrophysiology, computational fluid dynamics, fracture propagation, and weather prediction. Parallel processing is needed for simulations involving large-scale adaptive meshes. In this paper, we propose a parallel variational mesh quality improvement algorithm for use with distributed memory machines. Our parallel method is based on the sequential method by Huang, Ren, and Russell and the recent implementation by Huang and Kamenski. Their approach is based on the use of the Moving Mesh PDE method to adapt the mesh based on the minimization of an energy functional for mesh equidistribution and alignment. This leads to a system of ordinary differential equations (ODEs) to be solved which determine where to move the interior mesh nodes. The MMPDE method successfully removes/reduces the number of extreme dihedral angles, particularly those less than 20o or greater than 150o. An efficient solution is obtained by solving the ODEs on subregions of the mesh with overlapped communication and computation. Strong and weak scaling experiments on up to 128 cores for meshes with up to 160M elements demonstrate excellent results.

Automated summary

In this paper, a parallel variational mesh quality improvement algorithm for distributed memory machines is proposed. The algorithm adapts the mesh by using the Moving Mesh PDE method and solving a system of ordinary differential equations (ODEs) to determine the movement of interior mesh nodes. Strong and weak scaling experiments show excellent results for meshes with up to 160M elements on up to 128 cores.