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Full-Text Articles in Mathematics
Multigrid In A Weighted Space Arising From Axisymmetric Electromagnetics, Dylan M. Copeland, Jay Gopalakrishnan, Minah Oh
Multigrid In A Weighted Space Arising From Axisymmetric Electromagnetics, Dylan M. Copeland, Jay Gopalakrishnan, Minah Oh
Mathematics and Statistics Faculty Publications and Presentations
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 if the original three-dimensional domain is convex then the multigrid Vcycle applied to the inner product 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 …
A Multilevel Discontinuous Galerkin Method, Jay Gopalakrishnan, Guido Kanschat
A Multilevel Discontinuous Galerkin Method, Jay Gopalakrishnan, Guido Kanschat
Mathematics and Statistics Faculty Publications and Presentations
A variable V-cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented. An analysis under a mild regularity assumption shows that the preconditioner is uniform. The interior penalty method is then combined with a discontinuous Galerkin scheme to arrive at a discretization scheme for an advection-diffusion problem, for which an error estimate is proved. A multigrid algorithm for this method is presented, and numerical experiments indicating its robustness with respect to diffusion coefficient are reported.