scholarly journals Symbol-Based Multigrid Methods for Galerkin B-Spline Isogeometric Analysis

2017 ◽  
Vol 55 (1) ◽  
pp. 31-62 ◽  
Author(s):  
Marco Donatelli ◽  
Carlo Garoni ◽  
Carla Manni ◽  
Stefano Serra-Capizzano ◽  
Hendrik Speleers
Keyword(s):  
Isogeometric Analysis ◽  
Multigrid Methods ◽  
B Spline

B‐Spline‐Based Monotone Multigrid Methods

2007 ◽  
Vol 45 (3) ◽  
pp. 1175-1199 ◽  
Author(s):  
Markus Holtz ◽  
Angela Kunoth
Keyword(s):  
Multigrid Methods ◽  
B Spline

Multigrid methods for isogeometric analysis with THB-splines

2016 ◽  
Vol 308 ◽  
pp. 96-112 ◽  
Author(s):  
Clemens Hofreither ◽  
Bert Jüttler ◽  
Gábor Kiss ◽  
Walter Zulehner
Keyword(s):  
Isogeometric Analysis ◽  
Multigrid Methods

scholarly journals A priori error for unilateral contact problems with Lagrange multipliers and isogeometric analysis

2018 ◽  
Vol 39 (4) ◽  
pp. 1627-1651 ◽  
Author(s):  
Pablo Antolin ◽  
Annalisa Buffa ◽  
Mathieu Fabre
Keyword(s):  
Isogeometric Analysis ◽  
A Priori ◽  
Contact Problems ◽  
Unilateral Contact ◽  
Spline Space ◽  
Three Dimensions ◽  
B Spline ◽  
A Priori Error Estimate ◽  
The Stability ◽  
Unilateral Contact Problems

Abstract In this paper we consider a unilateral contact problem without friction between a rigid body and a deformable one in the framework of isogeometric analysis. We present the theoretical analysis of the mixed problem. For the displacement, we use the pushforward of a nonuniform rational B-spline space of degree $p$ and for the Lagrange multiplier, the pushforward of a B-spline space of degree $p-2$. These choices of space ensure the proof of an inf–sup condition and so on, the stability of the method. We distinguish between contact and noncontact sets to avoid the classical geometrical hypothesis of the contact set. An optimal a priori error estimate is demonstrated without assumption on the unknown contact set. Several numerical examples in two and three dimensions and in small and large deformation frameworks demonstrate the accuracy of the proposed method.

Sensitivity Analysis of Quality of B-spline Parameterization on Isogeometric Analysis

2021 ◽  
Author(s):  
Sangamesh Gondegaon ◽  
Hari Kumar Voruganti
Keyword(s):  
Isogeometric Analysis ◽  
Heat Conduction Problem ◽  
Exact Analytical Solution ◽  
Field Variable ◽  
Control Points ◽  
B Spline ◽  
Mesh Free ◽  
Spline Basis ◽  
Evaluation Metric

Isogeometric analysis (IGA) is a mesh free technique which make use of B-spline basis functions for geometry and field variable representation. Parameterization of B-spline for IGA is the counterpart of meshing as in finite element method (FEM). The objective of parameterization is to find the optimum set of control points for B-spline modelling. The position of control points of a B-spline model has huge effect on IGA results. In this work, the effect of B-spline parameterization on IGA result is presented. One dimensional case of bar with self-weight is solved and compared with exact analytical solution. First fundamental matrix is used as evaluation metric to check the quality of parameterization for 2-D domains. A heat conduction problem of a square domain is presented to study the parameterization effect for 2-D case.

Constructing B-spline solids from tetrahedral meshes for isogeometric analysis

2015 ◽  
Vol 35-36 ◽  
pp. 109-120 ◽  
Author(s):  
Hongwei Lin ◽  
Sinan Jin ◽  
Qianqian Hu ◽  
Zhenbao Liu
Keyword(s):  
Isogeometric Analysis ◽  
B Spline ◽  
Tetrahedral Meshes
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