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Multigrid solvers face multiple challenges on parallel computers. Twofundamental ones read as follows: Multiplicative solvers issue coarse gridsolves which exhibit low concurrency and many multigrid implementations sufferfrom an expensive coarse grid identification phase plus adaptive meshrefinement overhead. We propose a new additive multigrid variant forspacetrees, i.e. meshes as they are constructed from octrees and quadtrees: Itis an additive scheme, i.e. all multigrid resolution levels are updatedconcurrently. This ensures a high concurrency level, while the transferoperators between the mesh levels can still be constructed algebraically. Thenovel flavour of the additive scheme is an augmentation of the solver with anadditive, auxiliary damping parameter per grid level per vertex that is in turnconstructed through the next coarser level---an idea which utilises smoothedaggregation principles or the motivation behind AFACx: Per level, we solve anadditional equation whose purpose is to damp too aggressive solution updatesper vertex which would otherwise, in combination with all the other levels,yield an overcorrection and, eventually, oscillations. This additional equationis constructed additively as well, i.e. is once more solved concurrently to allother equations. This yields improved stability, closer to what is seen withmultiplicative schemes, while pipelining techniques help us to write down theadditive solver with single-touch semantics for dynamically adaptive meshes.

Stabilised Asynchronous Fast Adaptive Composite Multigrid using Additive Damping