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The concept of trimming, embedding, or immersing geometries into a computational background mesh has gained considerable attention in recent years, particularly in isogeometric analysis (IGA). In this approach, the physical domain is…

Numerical Analysis · Mathematics 2026-05-01 Christoph Hollweck , Andrea Gorgi , Nicolo Antonelli , Marcus Wagner , Roland Wüchner

Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…

Numerical Analysis · Mathematics 2018-12-05 Vitoriano Ruas

We present a novel isogeometric collocation method for solving the Poisson's and the biharmonic equation over planar bilinearly parameterized multi-patch geometries. The proposed approach relies on the use of a modified construction of the…

Numerical Analysis · Mathematics 2024-11-21 Mario Kapl , Aljaž Kosmač , Vito Vitrih

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 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

In the frame of isogeometric analysis, we consider a Galerkin boundary element discretization of the hyper-singular integral equation associated with the 2D Laplacian. We propose and analyze an adaptive algorithm which locally refines the…

Numerical Analysis · Mathematics 2020-03-03 Gregor Gantner , Dirk Praetorius , Stefan Schimanko

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

A novel approach which combines isogeometric collocation and an equilibrium-based stress recovery technique is applied to analyze laminated composite plates. Isogeometric collocation is an appealing strong form alternative to standard…

Numerical Analysis · Mathematics 2024-12-20 Alessia Patton , John-Eric Dufour , Pablo Antolin , Alessandro Reali

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

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

Most variational forms of isogeometric analysis use highly-continuous basis functions for both trial and test spaces. For a partial differential equation with a smooth solution, isogeometric analysis with highly-continuous basis functions…

Numerical Analysis · Mathematics 2019-02-12 Victor M. Calo , Quanling Deng , Sergio Rojas , Albert Romkes

Isogeometric Analysis is a high-order discretization method for boundary value problems that uses a number of degrees of freedom which is as small as for a low-order method. Standard isogeometric discretizations require a global…

Numerical Analysis · Mathematics 2021-03-05 Stefan Takacs

We consider isogeometric discretizations of the Poisson model problem, focusing on high polynomial degrees and strong hierarchical refinements. We derive a posteriori error estimates by equilibrated fluxes, i.e., vector-valued mapped…

Numerical Analysis · Mathematics 2024-03-01 Gregor Gantner , Martin Vohralík

We want to propose a new discretization ansatz for the second order Hessian complex exploiting benefits of isogeometric analysis, namely the possibility of high-order convergence and smoothness of test functions. Although our approach is…

Numerical Analysis · Mathematics 2021-09-14 Jeremias Arf , Bernd Simeon

The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…

Numerical Analysis · Mathematics 2023-06-09 Jochen Hinz , Ondine Chanon , Alessandra Arrigoni , Annalisa Buffa

In this work, we present an efficiently computational approach for designing material micro-structures by means of topology optimization. The central idea relies on using the isogeometric analysis integrated with the parameterized level set…

Computational Engineering, Finance, and Science · Computer Science 2023-07-19 Chuong Nguyen , Xiaoying Zhuang , Ludovic Chamoin , Hung Nguyen-Xuan , Xianzhong Zhao , Timon Rabczuk

In this work we define a spline complex preserving the cohomological structure of the continuous de Rham complex when the underlying physical domain is a toroidal solid. In the spirit of the isogeometric analysis, the spaces involved will…

Numerical Analysis · Mathematics 2025-01-07 Francesco Patrizi , Deepesh Toshniwal

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 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

Identifying spatial heterogeneous patterns has attracted a surge of research interest in recent years, due to its important applications in various scientific and engineering fields. In practice the spatially heterogeneous components are…

Methodology · Statistics 2024-05-07 Xin Zhang , Shan Yu , Zhengyuan Zhu , Xin Wang