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This work develops a computational framework that combines physics-informed neural networks with multi-patch isogeometric analysis to solve partial differential equations on complex computer-aided design geometries. The method utilizes…

Computational Engineering, Finance, and Science · Computer Science 2025-10-01 Moritz von Tresckow , Ion Gabriel Ion , Dimitrios Loukrezis

In this work, we study the approximation properties of multi-patch dG-IgA methods, that apply the multipatch Isogeometric Analysis (IgA) discretization concept and the discontinuous Galerkin (dG) technique on the interfaces between the…

Numerical Analysis · Mathematics 2014-08-04 Ulrich Langer , Ioannis Toulopoulos

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

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

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 present a framework for solving the triharmonic equation over bilinearly parameterized planar multi-patch domains by means of isogeometric analysis. Our approach is based on the construction of a globally $C^2$-smooth isogeometric spline…

Numerical Analysis · Mathematics 2018-08-21 Mario Kapl , Vito Vitrih

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline…

Numerical Analysis · Mathematics 2023-02-01 Cesare Bracco , Carlotta Giannelli , Mario Kapl , Rafael Vázquez

We present an isogeometric framework based on collocation to construct a $C^2$-smooth approximation of the solution of the Poisson's equation over planar bilinearly parameterized multi-patch domains. The construction of the used globally…

Numerical Analysis · Mathematics 2020-02-19 Mario Kapl , Vito Vitrih

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

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

This paper is concerned with the construction of graded meshes for approximating so-called singular solutions of elliptic boundary value problems by means of multipatch discontinuous Galerkin Isogeometric Analysis schemes. Such solutions…

Numerical Analysis · Mathematics 2015-12-03 Ulrich Langer , Angelos Mantzaflaris , Stephen E. Moore , Ioannis Toulopoulos

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

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

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

We study the dimension and construct a basis for $C^1$-smooth isogeometric function spaces over two-patch domains. In this context, an isogeometric function is a function defined on a B-spline domain, whose graph surface also has a B-spline…

Numerical Analysis · Mathematics 2017-01-24 Mario Kapl , Giancarlo Sangalli , Thomas 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 propose a new discontinuous Galerkin Isogeometric Analysis (IgA) technique for the numerical solution of elliptic diffusion problems in computational domains decomposed into volumetric patches with non-matching interfaces. Due to an…

Numerical Analysis · Mathematics 2015-11-19 Christoph Hofer , Ulrich Langer , Ioannis Toulopoulos

We construct over a given bilinear multi-patch domain a novel $C^s$-smooth mixed degree and regularity isogeometric spline space, which possesses the degree $p=2s+1$ and regularity $r=s$ in a small neighborhood around the edges and…

Numerical Analysis · Mathematics 2024-07-25 Mario Kapl , Aljaž Kosmač , Vito Vitrih

In this paper, we study the multi-patch discontinuous Galerkin isogeometric (DG-IGA) approximations for full-potential electronic structure calculations. We decompose the physical domain into several subdomains, represent each part of the…

Numerical Analysis · Mathematics 2024-12-16 Xiaoxu Li , Xucheng Meng

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