1 of 1

Fast and Flexible Monolithic AMG Framework for Multiphysics PDE Systems

Scientific Achievement

Develop a flexible framework that is easily adapted to multiphysics PDE systems.

Significance and Impact

Improved performance for solving linear systems corresponding to multiphysics PDE systems.

Research Details

• Implemented in MueLu, part of the Trilinos framework
• Designed for block matrices where the diagonal blocks correspond to different physics and the off-diagonal blocks represent the coupling between the physics blocks
• AMG components can be constructed independently for each physics block, or utilize information from other physics blocks depending on application needs
• Demonstratable numerical performance benefits for various MHD problems

​

​

Solver performance for the block monolithic AMG preconditioner AMG(BGS) with fixed damping parameter, 0.4, and 1 or 2 block Gauss-Seidel coupling iterations versus a more traditional fully coupled AMG preconditioner (FC-AMG) for an MHD generator example on a 480 × 32 × 32 mesh using 256 processors.

P. Ohm, T. Wiesner, E. Cyr, J. Hu, J. Shadid, R. Tuminaro, A monolithic algebraic multigrid framework for multiphysics applications with examples from resistive MHD. ETNA, 55:365-390, 2022.