Application of parallelized multigrid method to solution of MHD equilibrium with MPI

The potential of applying the multigrid method (MGM) to magnetohydrodynamics (MHD) equilibrium analysis is investigated. The nonlinear eigenvalue problem often appears when the MHD equilibria are determined by solving the Grad-Shafranov equation numerically. After linearizing the equation, the problem is solved using an iterative procedure. Although the SOR method or the Gauss-Seidel method is often used for the solution of the linearized equation, it takes much CPU time to solve the problem. We introduced the use of MGM instead of the conventional method for solving the linear equation. The parallel processing by using message passing interface (MPI) on a PC cluster is adopted for implementation of the MGM to achieve higher performance.