An Efficient Two-Grid Finite-Element Method of 3-D Nonlinear Magnetic-Field Computation

A two-grid finite-element method to reduce the computing time of nonlinear magnetic problems is presented. It is shown that the initial solution of the nonlinear iteration on the fine grid can be derived from the solutions of the coarse grid, thereby saving the computation time for iterations on the fine grid. A numerical technique based on the nonlinear functional is proposed to reduce the complexity of the discretization of the nonlinear term. The interpolation method from coarse grid to fine grid is discussed in this paper. A method to optimize the relaxation factor of Newton-Raphson iteration is also reported. The proposed method is applied to TEAM Workshop problem 13, and the results obtained by using the proposed algorithm are compared with those by using conventional methods.