Micro Abstract We present a framework for isogeometric analysis on unstructured quadrilateral meshes. Acknowledging the differing requirements posed by design and analysis, we propose the construction of a separate, smooth spline space for each, while ensuring isogeometric compatibility. A key ingredient in the approach is the use of singular parameterizations at extraordinary vertices. We demo...

We investigate geometric multigrid methods for solving the large, sparse linear systems which arise in isogeometric discretizations of elliptic partial differential equations. In particular, we study a smoother which incorporates the inverse of the mass matrix as an iteration matrix, and which we call mass-Richardson smoother. We perform a rigorous analysis in a model setting and perform some n...

We begin the mathematical study of Isogeometric Analysis based on NURBS (non-uniform rational B-splines.) Isogeometric Analysis is a generalization of classical Finite Element Analysis (FEA) which possesses improved properties. For example, NURBS are capable of more precise geometric representation of complex objects and, in particular, can exactly represent many commonly engineered shapes, suc...

We describe an approach to construct hexahedral solid NURBS (Non-Uniform Rational B-Splines) meshes for patient-specific vascular geometric models from imaging data for use in isogeometric analysis. First, image processing techniques, such as contrast enhancement, filtering, classification, and segmentation, are used to improve the quality of the input imaging data. Then, lumenal surfaces are e...

Article history: Available online 20 March 2015

Isogeometric Analysis (IGA) was introduced by Hughes et al. in 2005 [1] as a new method to bridge the gap between the geometry description and numerical analysis. Similar to the finite element approach, the IGA concept to solve a partial differential equation leads to a (linear) system of equations. The condition number of the coefficient matrix is a crucial factor for the stability of the syst...

Isogeometric analysis (IGA) has arisen as an attempt to unify the fields of CAD and classical finite element methods. The main idea of IGA consists in using for analysis the same functions (splines) that are used in CAD representation of the geometry. The main advantage with respect to the traditional finite element method is a higher smoothness of the numerical solution and more accurate repre...

We present a robust and efficient multigrid method for single-patch isogeometric discretizations using tensor product B-splines of maximum smoothness. Our method is based on a stable splitting of the spline space into a large subspace of “interior” splines which satisfy a robust inverse inequality, as well as one or several smaller subspaces which capture the boundary effects responsible for th...