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

Abstract

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 2 0 o or greater than 15 0 o . 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. • A parallel algorithm and implementation are proposed for variational mesh quality improvement on simplicial meshes. This is the first parallel variational mesh quality improvement method. • The method is based on the sequential moving mesh PDE (MMPDE) method of Huang, Ren, and Russell and the recent implementation by Huang and Kamenski which removes or significantly reduces the number of extreme dihedral angles in a tetrahedral mesh upon smoothing. • Their approach adapts the mesh based on the minimization of an energy functional for mesh equidistribution and alignment. This leads to a system of ODEs to be solved for the velocities of the interior mesh nodes. • An efficient solution is obtained by solving the ODEs in parallel on subregions of the mesh with overlapped communication and computation. • Excellent scalability results are obtained on up to 128 cores for tetrahedral meshes with up to 160M elements and on an industrial example from the tire industry.