Parallel Multigrid Methods on Manycore Clusters with IHKMcKernel The parallel multigrid method is expected to play an important role in largescale scientific computing on exascale supercomputer systems. Previously we proposed Hierarchical Coarse Grid Aggregation (hCGA), which dramatically improved the performance of the parallel multigrid solver when the number of MPI processes was O(104) or more. Because hCGA can handle only two layers of parallel hierarchical levels, the computation overhead due to coarse grid solver may become significant when the number of MPI processes reaches O(105) O(106) or more. In the present work, we propose AMhCGA (Adaptive Multilevel hCGA) that can take into account multiple layers of three or more levels, and show preliminary results using the OakforestPACS (OFP) system by JCAHPC. Additionally, we also examine the impact of a lightweight multikernel operating system, called IHKMcKernel, for parallel multigrid solvers running on OFP.

A multilevel approach for trace system in HDG discretizations Abstract   We propose a multilevel approach for trace systems resulting from hybridized discontinuous Galerkin (HDG) methods. The key is to blend ideas from nested dissection, domain decomposition, and highorder characteristic of HDG discretizations. Specifically, we first create a coarse solver by eliminating andor limiting the front growth in nested dissection. This is accomplished by projecting the trace data into a sequence of same or highorder polynomials on a set of increasingly hxe2x88x92coarser edgesfaces. We then combine the coarse solver with a blockJacobi fine scale solver to form a twolevel solverpreconditioner. Numerical experiments indicate that the performance of the resulting twolevel solverpreconditioner depends on the smoothness of the solution and can offer significant speedups and memory savings compared to the nested dissection direct solver. While the proposed algorithms are developed within the HDG framework, they are applicable to other hybrid(ized) highorder finite element methods. Moreover, we show that our multilevel algorithms can be interpreted as a multigrid method with specific intergrid transfer and smoothing operators. With several numerical examples from Poisson, pure transport, and convectiondiffusion equations we demonstrate the robustness and scalability of the algorithms with respect to solution order. While scalability with mesh size in general is not guaranteed and depends on the smoothness of the solution and the type of equation, improving it is a part of future work.