Related papers: Isogeometric analysis with $C^1$ hierarchical func…
We present an isogeometric framework based on collocation to construct a $C^2$-smooth approximation of the solution of the Poisson's equation over planar bilinearly parameterized multi-patch domains. The construction of the used globally…
In this paper, we consider $C^1$ cubic Powell-Sabin splines for the numerical solution of boundary value problems on planar and spatial surface domains. We first review the construction and basic properties of polynomial and rational $C^1$…
Isogeometric Analysis generalizes classical finite element analysis and intends to integrate it with the field of Computer-Aided Design. A central problem in achieving this objective is the reconstruction of analysis-suitable models from…
We prove $p$-robust approximation error estimates for $H^2$-conforming isogeometric discretizations over planar multi-patch domains. Possible applications are fourth order boundary value problems, like the biharmonic equation or…
A new construction of biorthogonal splines for isogeometric mortar methods is proposed. The biorthogonal basis has a local support and, at the same time, optimal approximation properties, which yield optimal results with mortar methods. We…
Spline functions have long been used in numerical solution of differential equations. Recently it revives as isogeometric analysis, which offers integration of finite element analysis and NURBS based CAD into a single unified process.…
Isogeometric analysis is a recently developed framework based on finite element analysis, where the simple building blocks in geometry and solution space are replaced by more complex and geometrically-oriented compounds. Box splines are an…
A particular class of planar two-patch geometries, called bilinear-like $G^{2}$ two-patch geometries, is introduced. This class includes the subclass of all bilinear two-patch parameterizations and possesses similar connectivity functions…
We analyze the space of geometrically continuous piecewise polynomial functions or splines for quadrangular and triangular patches with arbitrary topology and general rational transition maps. To define these spaces of G 1 spline functions,…
We present an isogeometric collocation method for solving the biharmonic equation over planar bilinearly parameterized multi-patch domains. The developed approach is based on the use of the globally $C^4$-smooth isogeometric spline space…
Geometrically continuous splines are piecewise polynomial functions defined on a collection of patches which are stitched together through transition maps. They are called $G^{r}$-splines if, after composition with the transition maps, they…
Isogeometric Analysis is a variant of the finite element method, where spline functions are used for the representation of both the geometry and the solution. Splines, particularly those with higher degree, achieve their full approximation…
We introduce a framework for spline spaces of hierarchical type, based on a parent-children relation, which is very convenient for the analysis as well as the implementation of adaptive isogeometric methods. Such framework makes it simple…
Complex geometries as common in industrial applications consist of multiple patches, if spline based parametrizations are used. The requirements for the generation of analysis-suitable models are increasing dramatically since isogeometric…
We study the space of $C^{2}$-smooth isogeometric functions on bilinearly parameterized multi-patch domains $\Omega \subset \mathbb{R}^{2}$, where the graph of each isogeometric function is a multi-patch spline surface of bidegree $(d,d)$,…
In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries consisting of a set of B-spline curves. Instead of forming the computational domain by a simple…
G-splines are a generalization of B-splines that deals with extraordinary points by imposing G^1 constraints across their spoke edges, thus obtaining a continuous tangent plane throughout the surface. Using the isoparametric concept and the…
We introduce here Cartesian splines or, for short, C-splines. C- splines are piecewise polynomials which are defined on adjacent Cartesian coordinate systems and are Cr continuous throughout. The Cr continuity is enforced by constraining…
Although isogeometric analysis exploits smooth B-spline and NURBS basis functions for the definition of discrete function spaces as well as for the geometry representation, the global smoothness in so-called multipatch parametrizations is…
The spline space $C_k^r(\Delta)$ attached to a subdivided domain $\Delta$ of $\R^{d} $ is the vector space of functions of class $C^{r}$ which are polynomials of degree $\le k$ on each piece of this subdivision. Classical splines on planar…