Developing Fast Solvers for Flagship MHD Tokamak Code M3D-C1
Scientific Achievement
Significance and Impact
Research Detail
To achieve algorithmic scalability (see figure), we added a scalable algorithm (multigrid) in the toroidal direction of the magnetohydrodynamics (MHD) code M3D-C1; this solution replaced the code’s approximate direct solver. We have also begun developing multigrid (MG) solvers for the poloidal plane.
M3D-C1 is the flagship MHD code in fusion energy sciences (FES) and depends on linear solvers for its fully implicit time integrators. Direct solvers are robust and mathematically simple but are well known to be theoretically suboptimal. Their deep data dependencies also hinder their effective use of modern, highly parallel hardware. Modern MG methods can potentially solve this scaling bottleneck in M3D-C1 and other FES MHD codes.
64-128 planes in production. Test 16 planes. FGMRES preconditioned with one semi-coarsening multigrid V(1,1) cycle. Smoother and coarse grid solver use original block Jacobi, LU sub-solver. Plot number of iterations vs number of coarse grids. 0 levels: old solver scaled down 5x to reflect cost of coarse grids and 2 fine grid smoother applications per level.
Four levels: true MG results results in one iteration. (not a direct solver)
Work performed at Princeton Plasma Physics Laboratory with LBNL
M3D-C1, as well as the FES-funded NIMROD code, use a regular toroidal grid structure in Tokamak models that we exploit with semi-coarsening MG (see figure). In addition to this toroidal solver, we are currently working with Princeton Plasma Physics Laboratory scientists to develop new fast and scalable poloidal plane solvers for highly anisotropic problems to deliver a complete fast MHD Tokamak solver for FES.
PI : Mark Adams (LBNL)
Collaborating Institutions: PPPL
DOE Program: FES
Program Manager: Michael Halfmoon
New multigrid solver
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