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Isogeometric Collocation: Cost Comparison with Galerkin Methods and Extension to Adaptive Hierarchical NURBS Discretizations
Author(s) -
Schillinger Dominik,
Evans John A.,
Reali Alessandro,
Scott Michael A.,
Hughes Thomas J.R.
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310049
Subject(s) - isogeometric analysis , collocation (remote sensing) , galerkin method , discretization , mathematics , discontinuous galerkin method , basis function , collocation method , quadrature (astronomy) , partial differential equation , degree of a polynomial , orthogonal collocation , polynomial , computer science , differential equation , mathematical analysis , ordinary differential equation , finite element method , physics , engineering , machine learning , electrical engineering , thermodynamics
Collocation 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)