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In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries consisting of a set of B-spline curves. Instead of forming the computational domain by a simple…

Computational Geometry · Computer Science 2017-11-22 Gang Xu , Ming Li , Bernard Mourrain , Timon Rabczuk , Jinlan Xu , Stephane P. A. Bordas

We propose a frictionless contact formulation for isogeometric analysis, which combines a collocated formulation for the contact surfaces with a standard Galerkin treatment of the bulk. We denote it as isogeometric Collocated Contact…

Computational Engineering, Finance, and Science · Computer Science 2022-04-04 Frederik Fahrendorf , Laura De Lorenzis

We consider large linear systems arising from the isogeometric discretization of the Poisson problem on a single-patch domain. The numerical solution of such systems is considered a challenging task, particularly when the degree of the…

Numerical Analysis · Mathematics 2016-07-22 Giancarlo Sangalli , Mattia Tani

We introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element…

Numerical Analysis · Mathematics 2019-05-21 Kosala Bandara , Fehmi Cirak

In this communication the advantages and drawbacks of the isogeometric analysis (IGA) are reviewed in the context of electromagnetic simulations. IGA extends the set of polynomial basis functions, commonly employed by the classical Finite…

Computational Engineering, Finance, and Science · Computer Science 2017-09-19 Zeger Bontinck , Jacopo Corno , Herbert De Gersem , Stefan Kurz , Andreas Pels , Sebastian Schöps , Felix Wolf , Carlo de Falco , Jürgen Dölz , Rafael Vázquez , Ulrich Römer

The perfectly matched layer (PML) formulation is a prominent way of handling radiation problems in unbounded domain and has gained interest due to its simple implementation in finite element codes. However, its simplicity can be advanced…

Numerical Analysis · Mathematics 2022-10-04 Jon Vegard Venås , Trond Kvamsdal

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

We analyze the space of geometrically continuous piecewise polynomial functions or splines for quadrangular and triangular patches with arbitrary topology and general rational transition maps. To define these spaces of G 1 spline functions,…

Algebraic Geometry · Mathematics 2016-03-24 Bernard Mourrain , Raimundas Vidunas , Nelly Villamizar

Isogeometric Analysis (IGA) bridges Computer-Aided Design (CAD) and Finite Element Analysis (FEA) by employing splines as a common basis for geometry and analysis. One of the advantages of IGA is in the realm of thin shell analysis: due to…

Numerical Analysis · Mathematics 2025-08-15 Hugo M. Verhelst , Angelos Mantzaflaris , Matthias Möller

A challenge in isogeometric analysis is constructing analysis-suitable volumetric meshes which can accurately represent the geometry of a given physical domain. In this paper, we propose a method to derive a spline-based representation of a…

Graphics · Computer Science 2017-03-22 Chiu Ling Chan , Cosmin Anitescu , Timon Rabczuk

In this work, a linear Kirchhoff-Love shell formulation in the framework of scaled boundary isogeometric analysis is presented that aims to provide a simple approach to trimming for NURBS-based shell analysis. To obtain a global C1-regular…

Numerical Analysis · Mathematics 2023-04-13 Mathias Reichle , Jeremias Arf , Bernd Simeon , Sven Klinkel

We introduce Gaussian quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. By definition, these spaces are of even degrees. The optimal quadrature rules we recently…

Numerical Analysis · Mathematics 2016-02-04 Michael Bartoň , Victor Manuel Calo

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

Geometrically continuous splines are piecewise polynomial functions defined on a collection of patches which are stitched together through transition maps. They are called $G^{r}$-splines if, after composition with the transition maps, they…

Numerical Analysis · Mathematics 2023-05-17 Angelos Mantzaflaris , Bernard Mourrain , Nelly Villamizar , Beihui Yuan

This work develops a computational framework that combines physics-informed neural networks with multi-patch isogeometric analysis to solve partial differential equations on complex computer-aided design geometries. The method utilizes…

Computational Engineering, Finance, and Science · Computer Science 2025-10-01 Moritz von Tresckow , Ion Gabriel Ion , Dimitrios Loukrezis

We investigate the isogeometric analysis for surface PDEs based on the extended Loop subdivision approach. The basis functions consisting of quartic box-splines corresponding to each subdivided control mesh are utilized to represent the…

Numerical Analysis · Mathematics 2019-11-06 Qing Pan , Timon Rabczuk , Gang Xu , Chong Chen

We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…

Numerical Analysis · Mathematics 2015-12-10 Christoph Lehrenfeld

In Isogeometric Analysis, the computational domain is often described as multi-patch, where each patch is given by a tensor product spline/NURBS parametrization. In this work we propose a FETI-like solver where local inexact solvers exploit…

Numerical Analysis · Mathematics 2020-09-23 Michal Bosy , Monica Montardini , Giancarlo Sangalli , Mattia Tani

The Isogeometric Analysis (IgA) of boundary value problems in complex domains often requires a decomposition of the computational domain into patches such that each of which can be parametrized by the so-called geometrical mapping. In this…

Numerical Analysis · Mathematics 2016-10-13 Christoph Hofer , Ulrich Langer , Ioannis Toulopoulos

Isogeometric Analysis is a variant of the finite element method, where spline functions are used for the representation of both the geometry and the solution. Splines, particularly those with higher degree, achieve their full approximation…

Numerical Analysis · Mathematics 2025-10-10 Stefan Takacs , Stefan Tyoler