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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

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

In structural optimization, both parameters and shape are relevant for the model performance. Yet, conventional optimization techniques usually consider either parameters or the shape separately. This work addresses this problem by…

Optimization and Control · Mathematics 2025-03-18 Michael Wiesheu , Theodor Komann , Melina Merkel , Sebastian Schöps , Stefan Ulbrich , Idoia Cortes Garcia

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

In this article we suggest two discretization methods based on isogeometric analysis (IGA) for planar linear elasticity. On the one hand, we apply the well-known ansatz of weakly imposed symmetry for the stress tensor and obtain a…

Numerical Analysis · Mathematics 2022-04-19 Jeremias Arf , Bernd Simeon

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

This contribution explores the combined capabilities of reduced basis methods and IsoGeometric Analysis (IGA) in the context of parameterized partial differential equations. The introduction of IGA enables a unified simulation framework…

Numerical Analysis · Mathematics 2025-10-14 Margarita Chasapi , Pablo Antolin , Annalisa Buffa

We consider dual-primal isogeometric tearing and interconnection (IETI-DP) solvers for multi-patch geometries in Isogeometric Analysis. Recently, the authors have published a convergence analysis for those solvers that is explicit in both…

Numerical Analysis · Mathematics 2021-03-09 Rainer Schneckenleitner , Stefan Takacs

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 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

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

We introduce a novel quadrature strategy for Isogeometric Analysis (IgA) boundary element discretizations, specifically tailored to collocation methods. Thanks to the dimensionality reduction and the natural handling of unbounded domains,…

Numerical Analysis · Mathematics 2025-11-25 Cesare Bracco , Francesco Patrizi , Alessandra Sestini

Multi-material problems often exhibit complex geometries along with physical responses presenting large spatial gradients or discontinuities. In these cases, providing high-quality body-fitted finite element analysis meshes and obtaining…

Numerical Analysis · Mathematics 2022-02-14 L. Noel , M. Schmidt , K. Doble , J. A. Evans , K. Maute

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

One of the important aspects of IsoGeometric Analysis (IGA) is the strong link between Computer Aided Design and analysis. Two of IGA'a major challenge are the assembly of patches (Constructive Solid Geometry geometries made of Boolean…

Numerical Analysis · Mathematics 2015-02-13 Michel Bercovier , Ilya Soloveichik

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 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

Isogeometrically enriched finite elements offer efficient localized isogeometric analysis (IGA) enrichment for numerical simulations involving large computational domains. This is achieved by employing surface enriched elements to interface…

Fluid Dynamics · Physics 2017-11-30 Raheel Rasool , Maximilian Harmel , Roger A. Sauer

An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies,…

Numerical Analysis · Computer Science 2015-02-04 Benjamin Marussig , Jürgen Zechner , Gernot Beer , Thomas-Peter Fries

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