An implicit energy-conservative 2D Fokker-Planck algorithm. II: Jacobian-free Newton-Krylov solver
[For part I, see the foregoing entry.] From the summary: We discuss efficient numerical implementation of an implicit energy-conservative scheme for multidimensional Fokker-Planck problems using multigrid-preconditioned Krylov methods. Results show that multigrid preconditioning is effective in speeding convergence and decreasing CPU requirements, particularly on fine meshes. The solver is demonstrated on grids up to \(128\times 128\) points in two-dimensional cylindrical velocity space \((v_r,v_p)\) with implicit time steps of the order of collisional time scale of the problem, \(\tau\). The method preserves particles exactly, and energy conservation is improved over alternative approaches, particularly in coarse meshes. Typical errors in the total energy over a time period of \(10\tau\) remain below a percent.
scientific article; zbMATH DE number 1422653
scientific article