New Paper on Multigrid Solvers

31 August 2022

Our new paper entitled "Non-invasive multigrid methods for semi-structured grids" has been published in the SIAM Journal of Scientific Computing. In this work, Dr. Matthias Mayr, along with collaborators from Sandia National Laboratories, proposes a mathematical framework called Region Multigrid that enables the application of algebraic multigrid (AMG) methods to semi-structured grids, exploiting the partial grid structure to obtain improved convergence and/or computational performance. In particular, this work distinguishes itself from previous work by other groups because it can be plugged into existing application codes without invasive changes to the existing code base ("non-invasive"). The developed algorithms are available via the open-source multigrid package MueLu within the Trilinos project.

Possible applications are numerous, ranging from simulations in plasma physics and fluid mechanics to problems in civil engineering. As an example, the paper analyzes the flow around a flying object during re-entry into the earth's atmosphere. This type of problem places particularly high demands on the meshing, which has pushed previous solution methods to their limits. The proposed region multigrid framework now allows for the first time the combination of multigrid methods and line-smoothing techniques, reducing the simulation time to about one third.

Link to the paper:

Bibliographic details: M. Mayr, L. Berger-Vergiat, P. Ohm, and R. S. Tuminaro. Non-invasive multigrid for semi-structured grids. SIAM Journal on Scientific Computing, 44(4):A2734–A2764, 2022