Colloquium Talk: Fault-tolerant Parallel Multigrid Method on Unaligned Adaptive Boundaries by Linda Stals
We are happy to announcement the colloquium talk:
Thursday, Jul 13, 2023, 13:00
Room 00.133, Cauerstrasse 11 (Animationslabor)
Speaker: Prof Linda Stals, Mathematical Sciences Institute, The Australian National University
Mercator fellow for FOR 5134: Solidification cracks during laser beam welding
Abstract:
As the generation of exascale high performance clusters begins, it has become evident that numerical algorithms will greatly benefit from built-in resilience features that can handle system faults. Prior studies of fault-tolerant multigrid methods have focused on structured grids. In this work, however, we study the resilience of multigrid solvers on unstructured grids with adaptive refinement. The challenge lies in the fact that unstructured grids distributed across multiple processors may manifest as local hierarchical grids with unaligned boundaries. Our numerical experiments highlight that this disparity can result in divergence when employing standard local multigrid for fault recovery. We analyse this phenomenon by using an energy control condition. To tackle the divergence issue, we propose a simple variation of the multigrid V-cycle that scales the coarse problem. By implementing this new method for local recovery, our numerical experiments confirm that convergence can be recovered on unstructured grids while the algorithm agrees with the standard multigrid V-cycle on grids with aligned boundaries. More importantly, the impact of a fault can be mitigated and delays in the global multigrid iterations can be reduced.