We consider a scalable implementation of multigrid methods for elliptic problems for fusion simulations on current and future high performance computer (HPC) architectures. Multigrid methods are the most efficient available solvers for elliptic problems. But, these methods require to handle the operations on several coarser levels where the communication costs are higher than the computation costs. We use only one core from a certain coarser level and get performance improvements on a large number of cores. Also, we consider the OpenMP/MPI hybridization implementation which is fitted on multi-core CPU architectures. The hybridization can use a small number of MPI tasks on the same number of cores and achieve performance improvements on a large number of cores. We investigate the scaling properties of the parallel multigrid solver with structured discretization on a regular hexagonal domain on a massively parallel computer (IFERC-CSC).
Kang, K. S. (2015). Scalable implementation of the parallel multigrid method on massively parallel computers. Computers and Mathematics with Applications, 70(11), 2701–2708. https://doi.org/10.1016/j.camwa.2015.07.023