Multigrid Methods
Parallel Algebraic Multigrid Domain Decomposition+
★Parallel AMG-DD breaking the communication wall★ Algebraic Multigrid (AMG) has optimal computational complexity but the cost of communication limits its scalability on large clusters. Algebraic Multigrid Domain Decomposition (AMG-DD) is an algorithm that trades some additional computations for a significant reduction in communication cost, resulting in superior performance on communication limited systems with high local compute power (e.g. GPU-cluster).
Parallel AMG, Krylov, multi-colored GS and ILU solvers+
★Comprehensive solver library for large GPU-clusters★ Algebraic multigrid is one of the main tools in science and industry for the solution of large sparse linear equation systems. The AmgX library executes AMG and Krylov methods with different preconditioners on GPU-systems with a single GPU, multiple GPUs and on GPU-clusters. Innovations in numerical schemes, graph algorithms and work scheduling enable the massively parallel execution.
Balanced Geometric Multigrid+
Neither solvers with best numerical convergence nor solvers with best parallel efficiency are the best choice for the fast solution of PDE problems in practice. The fastest solvers require a delicate balance between their numerical and hardware characteristics. Balancing both aspects we can even parallelize completely sequential preconditioners with large parallel speedup and hardly any loss in numerical performance.
GPU-Cluster Computing
★Minimally invasive acceleration of legacy code on GPU-clusters★ A single GPU already offers two levels of parallelism, but similar to CPUs, demand for higher performance and larger problem sizes leads to the utilization of GPU-clusters, in which every cluster node is equipped with GPUs. This adds the intra-node and inter-node parallelism. The main challenge for these heterogeneous systems is the enormous discrepancy in the bandwidth between the two finer and two coarser levels of parallelism and their integration in legacy code.