Magnetic Field Analysis With Nonconforming Voxel Modeling Using the Nested Geometric Multigrid Method

To establish a large scale magnetic field analysis, we have already proposed a magnetic field analysis using the first-order voxel modeling with nonconforming technique. The effectiveness of the nonconforming voxel modeling is shown using a simple 3-D eddy current model, a 2-D nonlinear IPM motor model, etc. In this paper, to make the proposed method more applicable for large scale analysis, the nested geometric multigrid method is introduced. First, to apply the multigrid method to the nonconforming finite element method, the treatments of the restriction and the prolongation are discussed. Then, the methods for nesting the fine mesh in the coarse mesh are discussed. Finally, the convergence characteristics of the multigrid method for the nonconforming voxel modeling are investigated using a simple 2-D magnetostatic model. It is shown that the essential convergence characteristic of the multigrid method can be obtained in the nonconforming voxel modeling when the restriction and the prolongation are treated appropriately and the geometries of models of the coarse and fine meshes are coincide with each other.