We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

Stabilized asynchronous fast adaptive composite multigrid using additive damping.

Murray, Charles D. and Weinzierl, Tobias (2021) 'Stabilized asynchronous fast adaptive composite multigrid using additive damping.', Numerical linear algebra with applications., 28 (3). e2328.


Multigrid solvers face multiple challenges on parallel computers. Two fundamental ones read as follows: Multiplicative solvers issue coarse grid solves which exhibit low concurrency and many multigrid implementations suffer from an expensive coarse grid identification phase plus adaptive mesh refinement overhead. We propose a new additive multigrid variant for spacetrees, that is, meshes as they are constructed from octrees and quadtrees: It is an additive scheme, that is, all multigrid resolution levels are updated concurrently. This ensures a high concurrency level, while the transfer operators between the mesh levels can still be constructed algebraically. The novel flavor of the additive scheme is an augmentation of the solver with an additive, auxiliary damping parameter per grid level per vertex that is in turn constructed through the next coarser level—an idea which utilizes smoothed aggregation principles or the motivation behind AFACx: Per level, we solve an additional equation whose purpose is to damp too aggressive solution updates per vertex which would otherwise, in combination with all the other levels, yield an overcorrection and, eventually, oscillations. This additional equation is constructed additively as well, that is, is once more solved concurrently to all other equations. This yields improved stability, closer to what is seen with multiplicative schemes, while pipelining techniques help us to write down the additive solver with single‐touch semantics for dynamically adaptive meshes.

Item Type:Article
Full text:(VoR) Version of Record
Available under License - Creative Commons Attribution.
Download PDF (Advance online version)
Publisher Web site:
Publisher statement:© 2020 The Authors. Numerical Linear Algebra with Applications published by John Wiley & Sons Ltd. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Date accepted:05 July 2020
Date deposited:25 August 2020
Date of first online publication:24 August 2020
Date first made open access:25 August 2020

Save or Share this output

Look up in GoogleScholar