Multigrid using Adaptive Unstructured Meshes for Massively Parallel Computation

摘要

This paper presents research to make massively parallel computations efficient for up to 8192 cores using unstructured meshes. While most massively parallel computations are performed subject to algorithmic constraints such as regular or structured grids it is less common to see massively parallel computation with adaptive unstructured meshes. Here the parallelization of the main components used to realize very large simulations of upto 10 billions of unknowns is presented using a muligrid method over unstructured mesh. First the strategy used to generate the computational meshes used during the multigrid resolution of a large linear systems is presented. Then the computation of the interpolation or restriction operators is considered. Finally some parallel performance indicators of the multigrid method for solving Stokes equation on a large range of cores from 1 to 8192 cores is presented. These indicators were from simulations completed on one the French national super computers Curie. In the last section a calculation completed on our own cluster using only 128 cores, is presented. This represents well, what has to be realized at a larger scale. It goes from reality to virtual, the micro structure used in the computation is a real one and it is used in our simulation, for doing that all the calculation.