Parallel Algebraic Multigrid for Fusion and Higher-Order PDEs
- Carleton College, Northfield, MN (United States)
- University of California, San Diego, CA (United States)
- University of Michigan, Ann Arbor, MI (United States)
- University of Cambridge (United Kingdom)
Multigrid methods play a key role in large-scale scientific simulation because they are among the fastest and most scalable approaches for solving the underlying sparse linear systems of equations that arise from a wide array of Partial Differential Equation (PDE) discretizations. Algebraic multigrid (AMG) is a special type of multigrid method that depends only on the description of the linear system, giving it better portability and broader applicability than geometric multigrid, as it requires no explicit knowledge of the problem geometry. Even though these methods are widely used today, there are still applications where further development is needed. In this report, we focus on PDEs with higher-order terms (e.g., fourth order), concentrating on a PDE that arises in tokamak edge plasma simulations (a tokamak is a machine that confines a plasma using magnetic fields and is believed to be the leading plasma confinement concept for future fusion power plants). General multigrid relaxes a linear system on coarser grids and reverses this process with interpolation, but standard AMG methods struggle with the aforementioned higher-order PDEs. We investigate cyclic coarsening and interpolation heuristics, as well as new iterative approximation methods of refining the solution at each grid to improve the existing multigrid approach. To this end, we ensure that these techniques are transferable to a parallelized setting with LLNL’s supercomputers.
- Research Organization:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- AC52-07NA27344
- OSTI ID:
- 2205732
- Report Number(s):
- LLNL-SR-857062; 1086828
- Country of Publication:
- United States
- Language:
- English
Similar Records
Non-Galerkin Coarse Grids for Algebraic Multigrid
Algebraic Multigrid Solvers for Coupled PDE Systems (Final Report – B619169)