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Isogeometric analysis has brought a paradigm shift in integrating computational simulations with geometric designs across engineering disciplines. This technique necessitates analysis-suitable parameterization of physical domains to fully…

Numerical Analysis · Mathematics 2024-03-18 Ye Ji , Matthias Möller , Yingying Yu , Chungang Zhu

We introduce manifold-based basis functions for isogeometric analysis of surfaces with arbitrary smoothness, prescribed $C^0$ continuous creases and boundaries. The utility of the manifold-based surface construction techniques in…

Numerical Analysis · Mathematics 2020-02-19 Qiaoling Zhang , Fehmi Cirak

The construction of volumetric parametrizations for computational domains is a key step in the pipeline of isogeometric analysis. Here, we investigate a solution to this problem based on the mesh deformation approach. The desired domain is…

Numerical Analysis · Mathematics 2019-03-25 Alexander Shamanskiy , Michael Helmut Gfrerer , Jochen Hinz , Bernd Simeon

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

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

Isogeometric analysis (IgA) uses the same class of basis functions for both, representing the geometry of the computational domain and approximating the solution. In practical applications, geometrical patches are used in order to get…

Numerical Analysis · Mathematics 2015-12-04 Ulrich Langer , Angelos Mantzaflaris , Stephen E. Moore , Ioannis Toulopoulos

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

We present an isogeometric collocation method for solving the biharmonic equation over planar bilinearly parameterized multi-patch domains. The developed approach is based on the use of the globally $C^4$-smooth isogeometric spline space…

Numerical Analysis · Mathematics 2023-12-25 Mario Kapl , Aljaž Kosmač , Vito Vitrih

This work focuses on the development of a super-penalty strategy based on the $L^2$-projection of suitable coupling terms to achieve $C^1$-continuity between non-conforming multi-patch isogeometric Kirchhoff plates. In particular, the…

Numerical Analysis · Mathematics 2020-07-29 Luca Coradello , Gabriele Loli , Annalisa Buffa

We present an adaptive scheme for isogeometric phase-field modeling, to perform suitably graded hierarchical refinement and coarsening on both single- and multi-patch geometries by considering truncated hierarchical spline constructions…

Numerical Analysis · Mathematics 2023-06-13 Cesare Bracco , Carlotta Giannelli , Alessandro Reali , Michele Torre , Rafael Vázquez

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

Given the spline representation of the boundary of a three dimensional domain, constructing a volumetric spline parameterization of the domain (i.e., a map from a unit cube to the domain) with the given boundary is a fundamental problem in…

Graphics · Computer Science 2020-01-08 Maodong Pan , Falai Chen , Weihua Tong

This work focuses on the coupling of trimmed shell patches using Isogeometric Analysis, based on higher continuity splines that seamlessly meet the $C^1$ requirement of Kirchhoff-Love-based discretizations. Weak enforcement of coupling…

Numerical Analysis · Mathematics 2024-04-15 Giuliano Guarino , Pablo Antolin , Alberto Milazzo , Annalisa Buffa

This work presents numerical techniques to enforce continuity constraints on multi-patch surfaces for three distinct problem classes. The first involves structural analysis of thin shells that are described by general Kirchhoff-Love…

Computational Engineering, Finance, and Science · Computer Science 2021-10-07 Karsten Paul , Christopher Zimmermann , Thang X. Duong , Roger A. Sauer

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

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 Laplace eigenvalue problem on circular sectors has eigenfunctions with corner singularities. Standard methods may produce suboptimal approximation results. To address this issue, a novel numerical algorithm that enhances standard…

Numerical Analysis · Mathematics 2025-05-16 Thomas Apel , Philipp Zilk

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 studies elasto-plastic large deformation behavior of thin shell structures using the isogeometric computational approach with the main focus on the efficiency in modelling the multi-patches and arbitrary material formulations. In…

Numerical Analysis · Mathematics 2023-07-12 Giang Huynh , Xiaoying Zhuang , Hoang-Giang Bui , G. Meschke , Hung Nguyen-Xuan

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