2015/06/20 by Markus Huber, Björn Gmeiner, Huber, Markus +5
Computer Science · #65N55 #65Y05 #68Q85 #Advanced Data Storage Technologies #Distributed and Parallel Computing Systems #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Numerical Analysis (math.NA) #Parallel Computing and Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1506.06185
openalex publication_date 2015/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Fault tolerant algorithms for the numerical approximation of elliptic partial differential equations on modern supercomputers play a more and more important role in the future design of exa-scale enabled iterative solvers. Here, we combine domain partitioning with highly scalable geometric multigrid schemes to obtain fast and fault-robust solvers in three dimensions. The recovery strategy is based on a hierarchical hybrid concept where the values on lower dimensional primitives such as faces are stored redundantly and thus can be recovered easily in case of a failure. The lost volume unknowns in the faulty region are re-computed approximately with multigrid cycles by solving a local Dirichlet problem on the faulty subdomain. Different strategies are compared and evaluated with respect to performance, computational cost, and speed up. Especially effective are strategies in which the local recovery in the faulty region is executed in parallel with global solves and when the local recovery is additionally accelerated. This results in an asynchronous multigrid iteration that can fully compensate faults. Excellent parallel performance on a current peta-scale system is demonstrated.