Algebraic Multigrid and Algebraic Reformulations of the Eddy Current Equation: Part II

Christopher Siefert

Sandia National Laboratories P.O. Box 5800, MS 1320 Albuquerque, NM 87185-1320

Pavel Bochev
Jonathan Hu
Ray Tuminaro


Abstract

With the rising popularity of compatible discretizations (edge elements) for the eddy current Maxwell's equations, there is a corresponding need for fast solvers. We propose an algebraic reformulation of the discrete system along with a new AMG technique for this reformulated problem. This transforms the curl-curl system into a block 2x2 system where the diagonal blocks are an edge Hodge Laplacian and a nodal scalar Laplacian, respectively. In this talk, we propose a solver for the edge Hodge Laplacian in the reformulated system. We introduce a special aggregation operator which transforms the system to a vector nodal problem on the coarse grid. We discuss the need for matrix-free smoothing on the fine level to reduce the computational cost. Finally, we present computational results for problems in both two and three dimensions. These examples include multimaterial problems with large jumps in material conductivity.