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Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are…

Numerical Analysis · Mathematics 2018-06-04 Qiaoling Zhang , Malcolm Sabin , Fehmi Cirak

An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies,…

Numerical Analysis · Computer Science 2015-02-04 Benjamin Marussig , Jürgen Zechner , Gernot Beer , Thomas-Peter Fries

This paper develops a unified theoretical framework for constructing B-spline basis function spaces with structural equivalence to finite element spaces. The theory rigorously establishes that these bases emerge as explicit linear…

Numerical Analysis · Mathematics 2026-01-29 Peng Yang , Maodong Pan , Falai Chen , Zhimin Zhang

We explain four variants of an adaptive finite element method with cubic splines and compare their performance in simple elliptic model problems. The methods in comparison are Truncated Hierarchical B-splines with two different refinement…

Numerical Analysis · Mathematics 2017-04-05 Paul Hennig , Markus Kästner , Philipp Morgenstern , Daniel Peterseim

Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…

Numerical Analysis · Mathematics 2025-01-30 Nils Wunsch , Keenan Doble , Mathias R. Schmidt , Lise Noël , John A. Evans , Kurt Maute

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

In the paper a recent enhancement to the open source package SfePy (Simple Finite Elements in Python, http://sfepy.org) is introduced, namely the addition of another numerical discretization scheme, the isogeometric analysis, to the…

Mathematical Software · Computer Science 2014-12-22 Robert Cimrman

In the context of isogeometric analysis, globally $C^1$ isogeometric spaces over unstructured quadrilateral meshes allow the direct solution of fourth order partial differential equations on complex geometries via their Galerkin…

Numerical Analysis · Mathematics 2018-12-24 Mario Kapl , Giancarlo Sangalli , Thomas Takacs

The paper outlines some recent developments of the boundary element method (BEM) that makes it more user friendly and suitable for a realistic simulation in geomechanics, especially for underground excavations and tunnelling. The…

Numerical Analysis · Mathematics 2021-01-25 Gernot Beer , Christian Duenser , Vincenzo Mallardo

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

In this paper hierarchical analysis-suitable T-splines (HASTS) are developed. The resulting spaces are a superset of both analysis-suitable T-splines and hierarchical B-splines. The additional flexibility provided by the hierarchy of…

Numerical Analysis · Mathematics 2015-06-19 Emily J. Evans , Michael A. Scott , Xin Li , Derek C. Thomas

This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby,…

Numerical Analysis · Mathematics 2024-09-02 Jochen Hinz

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

In this work a novel approach is presented for the isogeometric Boundary Element analysis of domains that contain inclusions with different elastic properties than the ones used for computing the fundamental solutions. In addition the…

Numerical Analysis · Computer Science 2016-08-24 Gernot Beer , Benjamin Marussig , Jürgen Zechner , Christian Dünser , Thomas-Peter Fries

This work proposes Isogeometric Analysis as an alternative to classical finite elements for simulating electric machines. Through the spline-based Isogeometric discretization it is possible to parametrize the circular arcs exactly, thereby…

Numerical Analysis · Mathematics 2018-03-14 Zeger Bontinck , Jacopo Corno , Sebastian Schöps , Herbert De Gersem

We introduce a framework for spline spaces of hierarchical type, based on a parent-children relation, which is very convenient for the analysis as well as the implementation of adaptive isogeometric methods. Such framework makes it simple…

Numerical Analysis · Mathematics 2018-08-08 Marcelo Actis , Pedro Morin , M. Sebastán Pauletti

We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…

Numerical Analysis · Mathematics 2017-05-16 Clemens Hofreither , Stefan Takacs , Walter Zulehner

Spline functions have long been used in numerical solution of differential equations. Recently it revives as isogeometric analysis, which offers integration of finite element analysis and NURBS based CAD into a single unified process.…

Numerical Analysis · Mathematics 2019-08-08 Guohui Zhao

Complex geometries as common in industrial applications consist of multiple patches, if spline based parametrizations are used. The requirements for the generation of analysis-suitable models are increasing dramatically since isogeometric…

Computational Engineering, Finance, and Science · Computer Science 2020-10-30 Christian Hesch , Ustim Khristenko , Rolf Krause , Alexander Popp , Alexander Seitz , Wolfgang Wall , Barbara Wohlmuth

Isogeometric Analysis generalizes classical finite element analysis and intends to integrate it with the field of Computer-Aided Design. A central problem in achieving this objective is the reconstruction of analysis-suitable models from…

Numerical Analysis · Mathematics 2022-11-09 Thomas Takacs , Deepesh Toshniwal