An Algebraic Multigrid Approach Based on a Compatible Gauge Reformulation of Maxwell's Equations

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 of the resulting linear algebraic systems. However, the traits that make compatible discretizations a preferred choice for the Maxwell's equations also render these linear systems essentially intractable by truly black-box techniques. We propose a new algebraic reformulation of the discrete eddy current equations along with a new algebraic multigrid technique (AMG) for this reformulated problem. The reformulation process takes advantage of a discrete Hodge decomposition on co-chains to replace the discrete eddy current equations by an equivalent 2

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: Pavel B. Bochev, Jonathan J. Hu, Christopher M. Siefert, Raymond S. Tuminaro
• Keywords: Current Equations, Eddy Current Equations, Finite Elements, SIAMSC 2008