An adaptive finite element scheme using multi-grid method for magnetostatic problems

A multigrid solver is developed to reduce computing time in the adaptive finite-element scheme. The meshes generated by the adaptive scheme can be directly used as multigrids for the computation. Elements in the adaptively generated grids are concentrated around the singular points, which makes the use of simple injection for restriction impossible. To overcome this problem, a weighted restriction is introduced. A magnetostatic field problem with a high degree of singularity is chosen as a case study. The multigrid method with weighted restriction reduces the computing time considerably compared with the well-known ICCG method. The computing time for problems where number of nodes is of the order of 10000 is reduced to 30%