Sandia National Laboratories

P.O. Box 969, MS 9217

Livermore, CA 94551

Sandia National Laboratories

P.O. Box 969, MS 9217

Livermore, CA 94551

Sandia National Laboratories

Computational Physics R&D

Sandia National Laboratories

P.O. Box 5800, MS 0819

Albuquerque, NM 87185-0819

Department of Mathematics

Box 19408

University of Texas at Arlington

Arlington, TX 76019-0408

Abstract

We consider the use of parallel algebraic multigrid for the solution of Maxwell's equations which are discretized via edge elements. The key difficulty is properly mapping the Curl operator's null space on to the coarse grids via a prolongation operator that is constructed using only algebraic information (i.e. matrix coefficients and a minimal amount of element information). The scheme that we consider is based on the work of Reitzinger and Schöberl as well as that of Hiptmair. This parallel multilevel preconditioner is implemented within the ML framework which already contains similar techniques like smoothed aggregation. The resulting iteration scheme is being integrated into a large complex parallel code that requires the repeated solution of the eddy current approximation to Maxwell's equations in a heterogeneous material properties environment as part of an overall Arbitrary Lagrangian-Eulerian magnetohydrodynamics algorithm. Numerical experiments are presented illustrating the efficiency of the approach on the ASCI Red machine in terms of both convergence and parallel speed-up.