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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

Isogeometric analysis (IGA) has emerged as a promising approach in the field of structural optimization, benefiting from the seamless integration between the computer-aided design (CAD) geometry and the analysis model by employing…

Optimization and Control · Mathematics 2024-07-02 Han Zhao , David Kamensky , John T. Hwang , Jiun-Shyan Chen

Topology optimization is a valuable tool in engineering, facilitating the design of optimized structures. However, topological changes often require a remeshing step, which can become challenging. In this work, we propose an isogeometric…

Numerical Analysis · Mathematics 2026-05-01 Guilherme Henrique Teixeira , Nepomuk Krenn , Peter Gangl , Benjamin Marussig

We propose a novel approach to the analysis of programmable geometrically exact shear deformable beam systems made of shape memory polymers. The proposed method combines the viscoelastic Generalized Maxwell model with the Williams, Landel…

Computational Engineering, Finance, and Science · Computer Science 2025-03-11 Giulio Ferri , Enzo Marino

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

The estimation of distributed parameters in partial differential equations (PDE) from measures of the solution of the PDE may lead to under-determination problems. The choice of a parameterization is a usual way of adding a-priori…

Numerical Analysis · Mathematics 2008-01-16 Hend Ben Ameur , François Clément , Pierre Weis , Guy Chavent

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

The finite element method (FEM) is commonly used in computational cardiac simulations. For this method, a mesh is constructed to represent the geometry and, subsequently, to approximate the solution. To accurately capture curved geometrical…

In isogeometric analysis, isogeometric function spaces are employed for accurately representing the solution to a partial differential equation (PDE) on a parameterized domain. They are generated from a tensor-product spline space by…

Numerical Analysis · Mathematics 2024-03-29 Dany Rios , Felix Scholz , Thomas Takacs

The study of quantum three-body problems has been centered on low-energy states that rely on accurate numerical approximation. Recently, isogeometric analysis (IGA) has been adopted to solve the problem as an alternative but more robust…

Numerical Analysis · Mathematics 2023-01-25 Danyang Li , Quanling Deng

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

A new methodology in isogeometric analysis (IGA) is presented. This methodology delivers low-cost variable-scale approximations (surrogates) of the matrices which IGA conventionally requires to be computed from element-scale quadrature…

Numerical Analysis · Mathematics 2020-08-11 Daniel Drzisga , Brendan Keith , Barbara Wohlmuth

The goal of this work is to improve focusing of high-intensity ultrasound by modifying the geometry of acoustic lenses through shape optimization. The shape optimization problem is formulated by introducing a tracking-type cost functional…

Optimization and Control · Mathematics 2017-12-15 Markus Muhr , Vanja Nikolić , Barbara Wohlmuth , Linus Wunderlich

In this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to…

Numerical Analysis · Mathematics 2020-11-23 Fabrizio Garotta , Nicola Demo , Marco Tezzele , Massimo Carraturo , Alessandro Reali , Gianluigi Rozza

This paper proposes an extension of the Multi-Index Stochastic Collocation (MISC) method for forward uncertainty quantification (UQ) problems in computational domains of shape other than a square or cube, by exploiting isogeometric analysis…

Numerical Analysis · Mathematics 2019-05-01 Joakim Beck , Lorenzo Tamellini , Raúl Tempone

We propose an Isogeometric approach for smoothing on surfaces, namely estimating a function starting from noisy and discrete measurements. More precisely, we aim at estimating functions lying on a surface represented by NURBS, which are…

Methodology · Statistics 2016-04-20 Matthieu Wilhelm , Luca Dedè , Laura M. Sangalli , Pierre Wilhelm

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 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

When solving a PDE problem numerically, a certain mesh-refinement process is always implicit, and very classically, mesh adaptivity is a very effective means to accelerate grid convergence. Similarly, when optimizing a shape by means of an…

Numerical Analysis · Mathematics 2015-09-11 Badr Abou El Majd

This paper focuses on optimization problems constrained by Parametric Variational Inequalities (PVI) defined on a moving set. Unlike most existing works on mathematical programs with equilibrium constraints, the equilibrium constraints have…

Optimization and Control · Mathematics 2026-03-06 Xiaojun Chen , Jin Zhang , Yixuan Zhang