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Related papers: Adaptive isogeometric methods with $C^1$ (truncate…

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Isogeometric Analysis is a spline-based discretization method to partial differential equations which shows the approximation power of a high-order method. The number of degrees of freedom, however, is as small as the number of degrees of…

Numerical Analysis · Mathematics 2021-04-22 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

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

In this paper we introduce a $C^1$ spline space over mixed meshes composed of triangles and quadrilaterals, suitable for FEM-based or isogeometric analysis. In this context, a mesh is considered to be a partition of a planar polygonal…

Numerical Analysis · Mathematics 2020-10-12 Jan Grošelj , Mario Kapl , Marjeta Knez , Thomas Takacs , Vito Vitrih

Invariant-based models for incompressible isotropic hyperelasticity are typically formulated as functions of the first and second invariants, $W = W(\bar{I}_1, \bar{I}_2)$. A widely used class of models employs separable representations of…

Computational Engineering, Finance, and Science · Computer Science 2026-04-14 Simon Wiesheier , Miguel Angel Moreno-Mateos , Paul Steinmann

An adaptive isogeometric method based on $d$-variate hierarchical spline constructions can be derived by considering a refine module that preserves a certain class of admissibility between two consecutive steps of the adaptive loop [6]. In…

Numerical Analysis · Mathematics 2016-05-04 Annalisa Buffa , Carlotta Giannelli , Philipp Morgenstern , Daniel Peterseim

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

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

Construction of spline surfaces from given boundary curves is one of the classical problems in computer aided geometric design, which regains much attention in isogeometric analysis in recent years and is called domain parameterization.…

Computational Geometry · Computer Science 2017-08-07 Maodong Pan , Falai Chen

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

We propose a local type of B-bar formulation, addressing locking in degenerated Reissner-Mindlin plate and shell formulations in the context of isogeometric analysis. Parasitic strain components are projected onto the physical space…

Computational Engineering, Finance, and Science · Computer Science 2018-02-23 Qingyuan Hu , Yang Xia , Sundararajan Natarajan , Andreas Zilian , Ping Hu , Stéphane P. A. Bordas

The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly…

Numerical Analysis · Mathematics 2021-07-21 Thibaut Hirschler , Pablo Antolin , Annalisa Buffa

Polynomial splines are ubiquitous in the fields of computer aided geometric design and computational analysis. Splines on T-meshes, especially, have the potential to be incredibly versatile since local mesh adaptivity enables efficient…

Algebraic Geometry · Mathematics 2019-03-15 Deepesh Toshniwal , Bernard Mourrain , Thomas Hughes

Multivariate B-splines and Non-uniform rational B-splines (NURBS) lack adaptivity due to their tensor product structure. Truncated hierarchical B-splines (THB-splines) provide a solution for this. THB-splines organize the parameter space…

Computational Engineering, Finance, and Science · Computer Science 2025-02-04 Andreas Grendas , Benjamin Marussig

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

The construction of robust solvers for linear systems obtained from the discretization of partial differential equations using Isogeometric Analysis is challenging since the condition number of the system matrix not only grows with the…

Numerical Analysis · Mathematics 2025-12-24 Monica Montardini , Stefan Takacs , Mattia Tani

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

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

Smoothing operation to make continuous density field from observed point-like distribution of galaxies is crucially important for topological or morphological analysis of the large-scale structure, such as, the genus statistics or the area…

Astrophysics · Physics 2016-08-30 Naoki Seto