Charles Murray presented his talk entitled “Lazy Stencil Integration in Multigrid Algorithms” at the ICG seminar this week. The talk abstract as follows:
Multigrid algorithms are among the most efficient solvers for elliptic partial differential equations. They are known to solve partial differential equations, e.g. the Poisson equation and related forms, in an optimal number of compute steps. However, we have to invest into an expensive matrix setup phase before we kick off the actual solve. This assembly effort is non-negligible and can delay the time to solution; particularly if the fine grid stencil integration is laborious. We propose to start multigrid solves with very inaccurate, geometric fine grid stencils which are then updated and improved in parallel to the actual solve. This update can be realised greedily and adaptively. We furthermore propose that any operator update propagates at most one level at a time, which ensures that multiscale information propagation does not hold back the actual solve. The increased asynchronity, i.e. the laziness, improves the runtime without a loss of stability if we make the grid update sequence take into account that multiscale operator information propagates at a finite speed.