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We present an isogeometric analysis technique that builds on manifold-based smooth basis functions for geometric modelling and analysis. Manifold-based surface construction techniques are well known in geometric modelling and a number of…

Numerical Analysis · Computer Science 2017-04-05 Musabbir Majeed , Fehmi Cirak

We study the dimension and construct a basis for $C^1$-smooth isogeometric function spaces over two-patch domains. In this context, an isogeometric function is a function defined on a B-spline domain, whose graph surface also has a B-spline…

Numerical Analysis · Mathematics 2017-01-24 Mario Kapl , Giancarlo Sangalli , Thomas Takacs

This work utilizes the Immersed Boundary Conformal Method (IBCM) to analyze Kirchhoff-Love and Reissner-Mindlin shell structures within an immersed domain framework. Immersed boundary methods involve embedding complex geometries within a…

Numerical Analysis · Mathematics 2024-08-06 Giuliano Guarino , Alberto Milazzo , Annalisa Buffa , Pablo Antolin

We study the space of $C^1$ isogeometric spline functions defined on trilinearly parameterized multi-patch volumes. Amongst others, we present a general framework for the design of the $C^1$ isogeometric spline space and of an associated…

Numerical Analysis · Mathematics 2021-10-06 Mario Kapl , Vito Vitrih

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…

Numerical Analysis · Mathematics 2017-08-22 Clemens Hofreither , Stefan Takacs

We present an open-source Python framework for the shape optimization of complex shell structures using isogeometric analysis (IGA). IGA seamlessly integrates computer-aided design (CAD) and analysis models by employing non-uniform rational…

Optimization and Control · Mathematics 2025-02-06 Han Zhao , John T. Hwang , Jiun-Shyan Chen

We present a new way to discretize a geometrically nonlinear elastic planar Cosserat shell. The kinematical model is similar to the general 6-parameter resultant shell model with drilling rotations. The discretization uses geodesic finite…

Numerical Analysis · Mathematics 2015-01-29 Oliver Sander , Patrizio Neff , Mircea Bîrsan

We present an isogeometric mortar method for the discretization of the biharmonic equation posed on multi-patch domains. We assume only $C^0$-conformity at interfaces and employs a mortar approach to weakly enforce $C^1$-continuity across…

Numerical Analysis · Mathematics 2025-10-08 Andrea Benvenuti , Gabriele Loli , Giancarlo Sangalli , Thomas Takacs

We present a new isogeometric method for the discretization of the Reissner-Mindlin plate bending problem. The proposed scheme follows a recent theoretical framework that makes possible to construct a space of smooth discrete deflections…

Numerical Analysis · Mathematics 2015-05-28 L. Beirão da Veiga , A. Buffa , C. Lovadina , M. Martinelli , G. Sangalli

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…

Numerical Analysis · Mathematics 2020-02-19 Mario Kapl , Vito Vitrih

Analysis-suitable $G^1$ (AS-$G^1$) multi-patch spline surfaces [4] are particular $G^1$-smooth multi-patch spline surfaces, which are needed to ensure the construction of $C^1$-smooth multi-patch spline spaces with optimal polynomial…

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

This paper presents a general, nonlinear isogeometric finite element formulation for rotation-free shells with embedded fibers that captures anisotropy in stretching, shearing, twisting and bending -- both in-plane and out-of-plane. These…

Computational Engineering, Finance, and Science · Computer Science 2023-06-06 Thang Xuan Duong , Mikhail Itskov , Roger Andrew Sauer

Isogeometric Analysis (IGA) is a computational technique for the numerical approximation of partial differential equations (PDEs). This technique is based on the use of spline-type basis functions, that are able to hold a global smoothness…

Numerical Analysis · Mathematics 2020-09-04 Álvaro Pé de la Riva , Carmen Rodrigo , Francisco J. Gaspar

We present a framework for solving the triharmonic equation over bilinearly parameterized planar multi-patch domains by means of isogeometric analysis. Our approach is based on the construction of a globally $C^2$-smooth isogeometric spline…

Numerical Analysis · Mathematics 2018-08-21 Mario Kapl , Vito Vitrih

The interaction between thin structures and incompressible Newtonian fluids is ubiquitous both in nature and in industrial applications. In this paper we present an isogeometric formulation of such problems which exploits a boundary…

Numerical Analysis · Mathematics 2017-02-17 Luca Heltai , Josef Kiendl , Antonio DeSimone , Alessandro Reali

In this work we develop a novel fully discrete version of the plates complex, an exact Hilbert complex relevant for the mixed formulation of fourth-order problems. The derivation of the discrete complex follows the discrete de Rham…

Numerical Analysis · Mathematics 2021-12-30 Daniele A. Di Pietro , Jérôme Droniou

We present a novel isogeometric collocation method for solving the Poisson's and the biharmonic equation over planar bilinearly parameterized multi-patch geometries. The proposed approach relies on the use of a modified construction of the…

Numerical Analysis · Mathematics 2024-11-21 Mario Kapl , Aljaž Kosmač , Vito Vitrih

Shells are ubiquitous thin structures that can undergo large nonlinear elastic deformations while exhibiting combined modes of bending and stretching, and have profound modern applications. In this paper, we have proposed a new Isogeometric…

Soft Condensed Matter · Physics 2022-06-22 Nikhil Padhye , Subodh Kalia

We present a comprehensive rotation-free Kirchhoff-Love (KL) shell formulation for peridynamics (PD) that is capable of modeling large elasto-plastic deformations and fracture in thin-walled structures. To remove the need for a predefined…

Numerical Analysis · Mathematics 2022-01-12 Masoud Behzadinasab , Mert Alaydin , Nathaniel Trask , Yuri Bazilevs

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline…

Numerical Analysis · Mathematics 2023-02-01 Cesare Bracco , Carlotta Giannelli , Mario Kapl , Rafael Vázquez