Dynamically Adaptive FAS for an Additively Damped AFAC Variant
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Multigrid solvers face multiple challenges on parallel computers. Two fundamental ones are that multiplicative solvers issue coarse grid solves which exhibit low concurrency and that many multigrid implementations suffer from an expensive coarse grid identification phase as well as dynamic adaptive mesh refinement (AMR) overhead. We therefore propose a new additive variant of the fast adaptive composite (FAC) method which can be combined with Full Approximation Storage (FAS) plus BoxMG inter-grid transfer operators on spacetrees. This allows for a straightforward realisation of arbitrary dynamic AMR on geometric multiscale grids with algebraic operators. The novel flavour of the additive scheme is an augmentation of the solver with an additive, auxiliary damping per grid level that is in turn constructed through the next coarser level---an idea which utilises smoothed aggregation principles or the motivation behind AFACx. This yields improved stability as we experience it with multiplicative schemes, while pipelining techniques help us to write down the additive solver with single-touch semantics.
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