Parallel multigrid 3D Maxwell solvers

Three-dimensional magnetic field problems are challenging not only because of interesting applications in the industry but also from the mathematical point of view. In the magnetostatic case, our Maxwell solver is based on a regularized mixed variational formulation of the Maxwell equations in H-0(c url) x H-0(1)(Omega) and their discretization by the Nedelec and Lagrange f inite elements. Eliminating the Lagrange multiplier from the mixed finite e lement equations, we arrive at a symmetric and positive definite (spd) prob lem that can be solved by some parallel multigrid preconditioned conjugate gradient (pcg) method. More precisely, this pcg solver contains a standard scaled Laplace multigrid regularizator in the regularization part and a spe cial multigrid preconditioner for the regularized Nedelec finite element eq uations that we want to solve. The parallelization of the pcg algorithm, th e Laplace multigrid regularizator and the multigrid preconditioner are base d on a unified domain decomposition data distribution concept. We present t he results of some numerical experiments on a parallel machine with distrib uted memory that show the high efficiency of our approach to real-life appl ications. (C) 2001 Elsevier Science B.V. All rights reserved.