English
Related papers

Related papers: An approximate $C^1$ multi-patch space for isogeom…

200 papers

The design of fast solvers for isogeometric analysis is receiving a lot of attention due to the challenge that offers to find an algorithm with a robust convergence with respect to the spline degree. Here, we analyze the application of…

Numerical Analysis · Mathematics 2018-06-18 Álvaro Pé de la Riva , Carmen Rodrigo , Francisco J. Gaspar

We propose an Isogeometric approach for smoothing on surfaces, namely estimating a function starting from noisy and discrete measurements. More precisely, we aim at estimating functions lying on a surface represented by NURBS, which are…

Methodology · Statistics 2016-04-20 Matthieu Wilhelm , Luca Dedè , Laura M. Sangalli , Pierre Wilhelm

This work presents numerical techniques to enforce continuity constraints on multi-patch surfaces for three distinct problem classes. The first involves structural analysis of thin shells that are described by general Kirchhoff-Love…

Computational Engineering, Finance, and Science · Computer Science 2021-10-07 Karsten Paul , Christopher Zimmermann , Thang X. Duong , Roger A. Sauer

Isogeometric analysis (IGA) has emerged as a promising approach in the field of structural optimization, benefiting from the seamless integration between the computer-aided design (CAD) geometry and the analysis model by employing…

Optimization and Control · Mathematics 2024-07-02 Han Zhao , David Kamensky , John T. Hwang , Jiun-Shyan Chen

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…

Numerical Analysis · Mathematics 2023-12-25 Mario Kapl , Aljaž Kosmač , Vito Vitrih

For Kichhoff-Love shell problems a new mixed formulation solely based on standard $H^1$ spaces is presented. This allows for flexibility in the construction of discretization spaces, e.g., standard $C^0$-coupling of multi-patch isogeometric…

Numerical Analysis · Mathematics 2019-01-30 Katharina Rafetseder , Walter Zulehner

We consider elliptic problems in multipatch isogeometric analysis (IGA) where the patch parameterizations may be singular. Specifically, we address cases where certain dimensions of the parametric geometry diminish as the singularity is…

Numerical Analysis · Mathematics 2025-07-30 Tobias Jonsson , Mats G. Larson , Karl Larsson

We present and analyze a stable space-time multi-patch discontinuous Galerkin Isogeometric Analysis (dG-IgA) scheme for the numerical solution of parabolic evolution equations in moving space-time computational domains. Following…

Numerical Analysis · Mathematics 2017-07-27 Stephen Edward Moore

This paper is concerned with the construction of graded meshes for approximating so-called singular solutions of elliptic boundary value problems by means of multipatch discontinuous Galerkin Isogeometric Analysis schemes. Such solutions…

Numerical Analysis · Mathematics 2015-12-03 Ulrich Langer , Angelos Mantzaflaris , Stephen E. Moore , Ioannis Toulopoulos

The analysis of electromagnetic scattering in the isogeometric analysis (IGA) framework based on Loop subdivision has long been restricted to simply-connected geometries. The inability to analyze multiply-connected objects is a glaring…

Numerical Analysis · Mathematics 2023-02-01 A. M. A. Alsnayyan , L. Kempel , B. Shanker

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…

Numerical Analysis · Mathematics 2019-01-30 Linus Wunderlich , Alexander Seitz , Mert Deniz Alaydin , Barbara Wohlmuth , Alexander Popp

Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The…

Numerical Analysis · Computer Science 2016-02-01 Vinh Phu Nguyen , Stéphane P. A. Bordas , Timon Rabczuk

Isogeometric analysis (IGA) enables exact representations of computational geometries and higher-order approximation of PDEs. In non-smooth domains, however, singularities near corners limit the effectiveness of IGA, since standard methods…

Numerical Analysis · Mathematics 2025-05-16 Thomas Apel , Philipp Zilk

A Nitche's method is presented to couple non-conforming two and three dimensional NURBS (Non Uniform Rational B-splines) patches in the context of isogeometric analysis (IGA). We present results for elastic stress analyses under the static…

Numerical Analysis · Mathematics 2016-02-01 Vinh Phu Nguyen , Pierre Kerfriden , Marco Brino , Stephane Bordas , Elvio Bonisoli

This paper studies elasto-plastic large deformation behavior of thin shell structures using the isogeometric computational approach with the main focus on the efficiency in modelling the multi-patches and arbitrary material formulations. In…

Numerical Analysis · Mathematics 2023-07-12 Giang Huynh , Xiaoying Zhuang , Hoang-Giang Bui , G. Meschke , Hung Nguyen-Xuan

In recent publications, the author and his coworkers have shown robust approximation error estimates for B-splines of maximum smoothness and have proposed multigrid methods based on them. These methods allow to solve the linear system…

Numerical Analysis · Mathematics 2021-03-05 Stefan Takacs

In this paper we introduce a $C^1$ spline space over mixed meshes composed of triangles and quadrilaterals, suitable for FEM-based or isogeometric analysis. In this context, a mesh is considered to be a partition of a planar polygonal…

Numerical Analysis · Mathematics 2020-10-12 Jan Grošelj , Mario Kapl , Marjeta Knez , Thomas Takacs , Vito Vitrih

Isogeometric analysis uses the same class of basis functions for both, representing the geometry of the computational domain and approximating the solution. In practical applications, geometrical patches are used in order to get flexibility…

Numerical Analysis · Mathematics 2014-02-11 Ulrich Langer , Stephen Edward Moore

In this work, we study the approximation properties of multi-patch dG-IgA methods, that apply the multipatch Isogeometric Analysis (IgA) discretization concept and the discontinuous Galerkin (dG) technique on the interfaces between the…

Numerical Analysis · Mathematics 2014-08-04 Ulrich Langer , Ioannis Toulopoulos

We propose the use of machine learning techniques to find optimal quadrature rules for the construction of stiffness and mass matrices in isogeometric analysis (IGA). We initially consider 1D spline spaces of arbitrary degree spanned over…

Numerical Analysis · Mathematics 2023-04-05 Tomas Teijeiro , Jamie M. Taylor , Ali Hashemian , David Pardo