Title: AMG for Reformulated Maxwell's Equations

Speaker: Chris Siefert, Sandia National Laboratories

Date/Time: Tuesday, October 31, 2006, 11:00 - 12:00 noon

Location:  CSRI Building/Room 90 (Sandia NM)

Brief Abstract: With the rise in popularity of compatible finite element, finite difference and finite volume discretizations for the time domain eddy current equations, there has been a corresponding need for fast solvers for the resulting linear algebraic systems.  Current solvers are often specialized techniques that cannot effectively leverage standard algebraic multigrid (AMG) methods and software for Laplace-type problems. We propose a new algebraic reformulation of the discrete eddy current equations along with a new AMG algorithm for this reformulated problem.  The reformulation process takes advantage of a discrete Hodge decomposition to replace the discrete eddy current equations by an equivalent block 2x2 linear system whose diagonal blocks are discrete Hodge Laplace operators acting on edges and nodes, respectively. While this new AMG technique requires some special treatment in generating a grid transfer from the fine mesh, the coarser meshes can be handled using standard methods for Laplace-type problems. Our new AMG method is applicable to a wide range of compatible methods on structured and unstructured grids, including edge finite elements, mimetic finite differences, co-volume methods and Yee-like schemes. We illustrate the new technique, using edge elements in the context of smoothed aggregation AMG, and present computational results for problems in both two and three dimensions.

CSRI POC: S. Scott Collis, (505) 284-1123