title: Multigrid methods for isogeometric discretization.
abstract: We present (geometric) multigrid methods for isogeometric discretization of scalar second order elliptic problems. The smoothing property of the relaxation method, and the approximation property of the intergrid transfer operators are analyzed. These properties, when used in the framework of classical multigrid theory, imply uniform convergence of two-grid and multigrid methods. Supporting numerical results are provided for the smoothing property, the approximation property, convergence factor and iterations count forV-,W- andF-cycles, and the linear dependence ofV-cycle convergence on the smoothing steps. For two dimensions, numerical results include the problems with variable coefficients, simple multi-patch geometry, a quarter annulus, and the dependence of convergence behavior on refinement levels [Formula: see text], whereas for three dimensions, only the constant coefficient problem in a unit cube is considered. The numerical results are complete up to polynomial order [Formula: see text], and for [Formula: see text] and [Formula: see text] smoothness.
authors: Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, 4040 Linz, Austria.
authors: K P S
authors: KP
authors: Gahalaut
authors: Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, 4040 Linz, Austria.
authors: J K
authors: JK
authors: Kraus
authors: Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, 4040 Linz, Austria.
authors: S K
authors: SK
authors: Tomar
keywords: B-splines; Galerkin formulation; Isogeometric method; Multigrid method; NURBS