Mesh partitioning using matrix value approximations for parallel computational fluid dynamics simulations

Mesh partitioning is significant to the efficiency of parallel computational fluid dynamics simulations. The most time-consuming parts of parallel computational fluid dynamics simulations are iteratively solving linear systems derived from partial differential equation discretizations. This article aims at mesh partitioning for better iterative convergence feature of this procedure. For typical computational fluid dynamics simulations in which partial differential equations are discretized and solved after the mesh is partitioned, numerical information of the linear systems is not available yet during mesh partitioning. We propose to construct approximations for matrix elements and theoretically find out that for finite-volume-based problems, the face area can approximate the corresponding matrix element well. A mesh partitioning scheme using the matrix value approximations for better iterative convergence behavior is implemented and numerically testified. The results show that our method can capture the most important factor influencing the matrix values and achieve partitions with good performance throughout the simulations with non-uniform meshes. The novel partitioning strategy is general and easy to implement in various partitioning packages.