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We present a novel method for isogeometric analysis (IGA) to directly work on geometries constructed by Boolean operations including difference (i.e., trimming), union and intersection. Particularly, this work focuses on the union…

Numerical Analysis · Mathematics 2019-12-16 Pablo Antolin , Annalisa Buffa , Riccardo Puppi , Xiaodong Wei

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 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 $(d,d)$,…

Numerical Analysis · Mathematics 2017-01-25 Mario Kapl , Vito Vitrih

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

In this paper, we develop multigrid solvers for the biharmonic problem in the framework of isogeometric analysis (IgA). In this framework, one typically sets up B-splines on the unit square or cube and transforms them to the domain of…

Numerical Analysis · Mathematics 2019-06-18 Jarle Sogn , Stefan Takacs

The first step towards applying isogeometric analysis techniques to solve PDE problems on a given domain consists in generating an analysis-suitable mapping operator between parametric and physical domains with one or several patches from…

Numerical Analysis · Mathematics 2019-10-29 Jochen Hinz , Matthias Möller , Cornelis Vuik

This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main…

Numerical Analysis · Mathematics 2017-07-11 Elena Atroshchenko , Gang Xu , Satyendra Tomar , Stephane P. A. Bordas

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

Isogeometric Analysis is a high-order discretization method for boundary value problems that uses a number of degrees of freedom which is as small as for a low-order method. Standard isogeometric discretizations require a global…

Numerical Analysis · Mathematics 2021-03-05 Stefan Takacs

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…

Numerical Analysis · Mathematics 2017-07-24 Mario Kapl , Vito Vitrih

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…

Numerical Analysis · Mathematics 2022-11-09 Thomas Takacs , Deepesh Toshniwal

This paper deals with a special class of parametrizations for Isogeometric Analysis (IGA). The so-called scaled boundary parametrizations are easy to construct and particularly attractive if only a boundary description of the computational…

Numerical Analysis · Mathematics 2017-11-22 Clarissa Arioli , Alexander Shamanskiy , Sven Klinkel , Bernd Simeon

Isogeometric Analysis (IgA) is a framework for setting up spline-based discretizations of partial differential equations, which has been introduced around a decade ago and has gained much attention since then. If large spline degrees are…

Numerical Analysis · Mathematics 2021-03-05 Christoph Hofer , Stefan Takacs

Isogeometric analysis (IGA) is a numerical method that connects computer-aided design (CAD) with finite element analysis (FEA). In CAD the computational domain is usually represented by B-spline or NURBS patches. Given a NURBS…

Numerical Analysis · Mathematics 2023-10-04 Somayeh Kargaran , Bert Jüttler , Thomas Takacs

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…

Computational Engineering, Finance, and Science · Computer Science 2023-03-22 Zuowei Wen , Md. Sadman Faruque , Xin Li , Xiaodong Wei , Hugo Casquero

In the Isogeometric Analysis (IGA) framework, the computational domain has very often a multipatch representation. The multipatch domain can be obtained by a volume segmentation of a boundary represented domain, e.g., provided by a Computer…

Numerical Analysis · Mathematics 2018-03-28 Christoph Hofer , Ioannis Toulopoulos

A simple skew-symmetric Nitsche's formulation is introduced into the framework of isogeometric analysis (IGA) to deal with various problems in small strain elasticity: essential boundary conditions, symmetry conditions for Kirchhoff plates,…

Numerical Analysis · Mathematics 2018-08-15 Qingyuan Hu , Franz Chouly , Ping Hu , Gengdong Cheng , Stéphane Pierre Alain Bordas

Isogeometric analysis (IGA) is used to simulate a permanent magnet synchronous machine. IGA uses non-uniform rational B-splines to parametrise the domain and to approximate the solution space, thus allowing for the exact description of the…

Computational Engineering, Finance, and Science · Computer Science 2017-08-09 Zeger Bontinck , Jacopo Corno , Prithvi Bhat , Herbert De Gersem , Sebastian Schöps

This paper presents spline-based coupling methods for partitioned multiphysics simulations, specifically designed for isogeometric analysis (IGA) based solvers. Traditional vertex-based coupling approaches face significant challenges when…

Numerical Analysis · Mathematics 2025-05-27 Jing-Ya Li , Hugo M. Verhelst , Henk den Besten , Matthias Möller

We introduce manifold-based basis functions for isogeometric analysis of surfaces with arbitrary smoothness, prescribed $C^0$ continuous creases and boundaries. The utility of the manifold-based surface construction techniques in…

Numerical Analysis · Mathematics 2020-02-19 Qiaoling Zhang , Fehmi Cirak