Seventh Copper Mountain Conference on Multigrid Methods

The Seventh Copper Mountain Conference on Multigrid Methods was held on 2-7 Apr. 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection shows its rapid trend to further diversity and depth

Seventh Copper Mountain Conference on Multigrid Methods

The Seventh Copper Mountain Conference on Multigrid Methods was held on April 2-7, 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The vibrancy and diversity in this field are amply expressed in these important papers, and the collection clearly shows the continuing rapid growth of the use of multigrid acceleration techniques

Asynchronous Stabilisation and Assembly Techniques for Additive Multigrid

Multigrid solvers are among the best solvers in the world, but once applied in the real world there are issues they must overcome. Many multigrid phases exhibit low concurrency. Mesh and matrix assembly are challenging to parallelise and introduce algorithmic latency. Dynamically adaptive codes exacerbate these issues. Multigrid codes require the computation of a cascade of matrices and dynamic adaptivity means these matrices are recomputed throughout the solve. Existing methods to compute the matrices are expensive and delay the solve. Non- trivial material parameters further increase the cost of accurate equation integration. We propose to assemble all matrix equations as stencils in a delayed element-wise fashion. Early multigrid iterations use cheap geometric approximations and more accurate updated stencil integrations are computed in parallel with the multigrid cycles. New stencil integrations are evaluated lazily and asynchronously fed to the solver once they become available. They do not delay multigrid iterations. We deploy stencil integrations as parallel tasks that are picked up by cores that would otherwise be idle. Coarse grid solves in multiplicative multigrid also exhibit limited concurrency. Small coarse mesh sizes correspond to small computational workload and require costly synchronisation steps. This acts as a bottleneck and delays solver iterations. Additive multigrid avoids this restriction, but becomes unstable for non-trivial material parameters as additive coarse grid levels tend to overcorrect. This leads to oscillations. We propose a new additive variant, adAFAC-x, with a stabilisation parameter that damps coarse grid corrections to remove oscillations. Per-level we solve an additional equation that produces an auxiliary correction. The auxiliary correction can be computed additively to the rest of the solve and uses ideas similar to smoothed aggregation multigrid to anticipate overcorrections. Pipelining techniques allow adAFAC-x to be written using single-touch semantics on a dynamically adaptive mesh