Multigrid in a weighted space arising from axisymmetric electromagnetics

Consider the space of two dimensional vector functions whose components and curl are square integrable with respect to the degenerate weight given by the radial variable. This space arises naturally when modeling electromagnetic problems under axial symmetry and performing a dimension reduction via cylindrical coordinates. We prove that the multigrid V-cycle applied to the innerproduct in this space converges, provided certain modern smoothers are used. For the convergence analysis, we first prove several intermediate results, e.g., the approximation properties of a commuting projector in weighted norms, and a superconvergence estimate for a dual mixed method in weighted spaces. The uniformity of the multigrid convergence rate with respect to meshsize is then established theoretically and illustrated through numerical experiments.

• Type: Journal
• Year: 2010
• Where: MOC
• Authors: Dylan M. Copeland, Jayadeep Gopalakrishnan, Minah Oh
• Keywords: Certain Modern Smoothers, Dimensional Vector Functions, MOC 2010, Multigrid Convergence Rate, Security Privacy