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Trimming techniques are efficient ways to generate complex geometries in Computer-Aided Design(CAD). In this paper, an improved isogeometric analysis(IGA) method for trimmed geometries is proposed. We will show that the proposed method…

Numerical Analysis · Computer Science 2017-07-04 Jinlan Xu , Ningning Sun , Laixin Shu , Timon Rabczuk , Gang Xu

Isogeometric analysis (IgA) offers enhanced approximation capabilities for the discretization of elliptic boundary-value problems, yet it results in large, sparse, and increasingly ill-conditioned linear systems due to higher…

Numerical Analysis · Mathematics 2026-05-01 Pasqua D'Ambra , Fabio Durastante , Salvatore Filippone

This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the…

Numerical Analysis · Mathematics 2022-11-18 Annalisa Buffa , Gregor Gantner , Carlotta Giannelli , Dirk Praetorius , Rafael Vázquez

This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the…

Numerical Analysis · Mathematics 2020-01-30 Jochen Hinz , Andrzej Jaeschke , Matthias Möller , Cornelis Vuik

Isogeometric analysis is a recently developed framework based on finite element analysis, where the simple building blocks in geometry and solution space are replaced by more complex and geometrically-oriented compounds. Box splines are an…

Numerical Analysis · Mathematics 2019-09-26 Tadej Kanduc , Carlotta Giannelli , Francesca Pelosi , Hendrik Speleers

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 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

Complex geometries as common in industrial applications consist of multiple patches, if spline based parametrizations are used. The requirements for the generation of analysis-suitable models are increasing dramatically since isogeometric…

Computational Engineering, Finance, and Science · Computer Science 2020-10-30 Christian Hesch , Ustim Khristenko , Rolf Krause , Alexander Popp , Alexander Seitz , Wolfgang Wall , Barbara Wohlmuth

This contribution investigates the connection between Isogeometric Analysis (IgA) and the Partial Element Equivalent Circuit (PEEC) method for electrostatic problems. We demonstrate that using the spline-based geometry concepts from IgA…

Computational Engineering, Finance, and Science · Computer Science 2022-09-30 Riccardo Torchio , Maximilian Nolte , Sebastian Schöps , Albert E. Ruehli

We present an approximately $C^1$-smooth multi-patch spline construction which can be used in isogeometric analysis (IGA). A key property of IGA is that it is simple to achieve high order smoothness within a single patch. To represent more…

Numerical Analysis · Mathematics 2022-10-12 Pascal Weinmüller , Thomas Takacs

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

Adaptive isogeometric methods for the solution of partial differential equations rely on the construction of locally refinable spline spaces. A simple and efficient way to obtain these spaces is to apply the multi-level construction of…

Numerical Analysis · Mathematics 2019-09-25 Cesare Bracco , Carlotta Giannelli , Mario Kapl , Rafael Vázquez

Volumetric spline parameterization and computational efficiency are two main challenges in isogeometric analysis (IGA). To tackle this problem, we propose a framework of computation reuse in IGA on a set of three-dimensional models with…

Numerical Analysis · Computer Science 2016-09-02 Gang Xu , Tsz-Ho Kwok , Charlie C. L. Wang

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

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

We propose a framework for solving partial differential equations (PDEs) motivated by isogeometric analysis (IGA) and local tensor-product splines. Instead of using a global basis for the solution space we use as generators the disjoint…

Numerical Analysis · Mathematics 2024-09-02 Andrea Bressan , Massimiliano Martinelli , Giancarlo Sangalli

An Isogeometric Boundary Element Method (IgA-BEM) is considered for the numerical solution of Helmholtz problems on 3D bounded or unbounded domains, admitting a smooth conformal multi-patch representation of their finite boundary surface.…

Numerical Analysis · Mathematics 2022-12-26 Antonella Falini , Tadej Kanduc , Maria Lucia Sampoli , Alessandra Sestini

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 a new discontinuous Galerkin Isogeometric Analysis (IgA) technique for the numerical solution of elliptic diffusion problems in computational domains decomposed into volumetric patches with non-matching interfaces. Due to an…

Numerical Analysis · Mathematics 2015-11-19 Christoph Hofer , Ulrich Langer , Ioannis Toulopoulos

We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…

Numerical Analysis · Mathematics 2017-05-16 Clemens Hofreither , Stefan Takacs , Walter Zulehner