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Refinement Algorithms for Adaptive Isogeometric Methods with Hierarchical Splines

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Mathematical analysis of variational isogeometric methods

Annalisa Buffa, Rafael Vazquez Hernandez

This review paper collects several results that form part of the theoretical foundation of isogeometric methods. We analyse variational techniques for the numerical resolution of PDEs based on splines or NURBS and we provide optimal approximation and error ...

2014

Analysis-suitable T-splines of arbitrary degree: definition, linear independence and approximation properties

Annalisa Buffa, Rafael Vazquez Hernandez

T-splines are an important tool in IGA since they allow local refinement. In this paper we define analysis-suitable T-splines of arbitrary degree and prove fundamental properties: Linear independence of the blending functions and optimal approximation prop ...

2013

Characterization of T-splines with reduced continuity order on T-meshes

Annalisa Buffa, Mithlesh Kumar

The use of T-splines [30] in Isogeometric Analysis [24] has been proposed in [5] as a tool to enhance the flexibility of isogeometric methods. If T-splines are a very general concept, their success in isogeometric analysis relies upon some basic properties ...

2012

Isogeometric Analysis and the Finite Cell method

Luca Dede'

The finite cell method (FCM) belongs to the class of immersed boundary methods, and combines the fictitious domain approach with high-order approximation, adaptive integration and weak imposition of unfitted Dirichlet boundary conditions. Its main idea con ...

2012

Some estimates for h-p-k-refinement in isogeometric analysis

Annalisa Buffa

In this paper, we propose a theoretical study of the approximation properties of NURBS spaces, which are used in Isogeometric Analysis. We obtain error estimates that are explicit in terms of the mesh-size h, the degree p and the global regularity, measure ...

2011

Limit laws of transient excited random walks on integers

Thomas Mountford

We consider excited random walks (ERWs) on Z with a bounded number of i.i.d. cookies per site without the non-negativity assumption on the drifts induced by the cookies. Kosygina and Zerner [15] have shown that when the total expected drift per site, delta ...

2011

Modélisation géométrique itérative sous contraintes

Gilles Gouaty

Iterative models are widely used today in CAD. They allow, with a limited number of parameters, to represent relatively complex forms through a subdivision algorithm. There is a wide variety of such models (Catmull-Clark, Doo-Sabin, L-Systems...). Most ite ...

EPFL2010

Multiscale algorithm with patches of finite elements and applications

Vittoria Augusta Rezzonico Janka

We develop a discretisation and solution technique for elliptic problems whose solutions may present strong variations, singularities, boundary layers and oscillations in localised regions. We start with a coarse finite element discretisation with a mesh s ...

EPFL2007

Geometric modeling based on triangle meshes

Mark Pauly

This course is designed to cover the entire geometry processing pipeline based on triangle meshes. We will present the latest concepts for mesh generation and mesh repair, for geometry and topology optimizations like mesh smoothing, decimation, and remeshi ...

2006

Implicit meshes

Slobodan Ilic

This thesis proposes novel ways both to represent the static surfaces, and to parameterize their deformations. This can be used both by automated algorithms for efficient 3–D shape reconstruction, and by graphics designers for editing and animation. Deform ...

EPFL2005