Isogeometric collocation: Cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations

• DOI: 10.1016/j.cma.2013.07.017
• Publication Date: 2013-08-08T01:51:35Z
• Authors: Dominik Schillinger; John A. Evans; Alessandro Reali; Michael A. Scott; Thomas J.R. Hughes
• Keywords: Isogeometric analysis; Reduced quadrature; Isogeometric collocation methods; 0211 other engineering and technologies; Local adaptivity; Weighted collocation; Hierarchical refinement of NURBS; 02 engineering and technology; 620; 510

AbstractCollocation is based on the discretization of the strong form of the underlying partial differential equations, which requires basis functions of sufficient order and smoothness. Consequently, the use of isogeometric analysis (IGA) for collocation suggests itself, since splines can be readily adjusted to any order in polynomial degree and continuity required by the differential operators. In addition, they can be generated for domains of arbitrary geometric and topological complexity, directly linked to and fully supported by CAD technology. The major advantage of isogeometric collocation over Galerkin type IGA is the minimization of the computational effort for numerical quadrature. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)