Application of multilevel preconditioners to finite element magnetostatic problems

Iterative methods based ran Xu's Multilevel Preconditioners (MP) for finite element problems have recently been studied in mathematical literature. For these methods the number of iterations grows only as a logarithm of the number of nodes. Therefore for fine meshes the MP method is faster than more traditional algorithms (such as ICCG or Nested Dissection). The present paper examines practical application of MP and shows the importance of weighting factors and of the inverse operator at the coarsest level. Numerical examples for test and real-life problems are presented.>