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We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations in arbitrary space dimension $d\ge2$. We employ…

Numerical Analysis · Mathematics 2017-11-20 Gregor Gantner , Daniel Haberlik , Dirk Praetorius

In this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on NURBS. The motivation for this work is an integrated and complete work pipeline from CAD to parametrization of domain geometry, then…

Numerical Analysis · Mathematics 2017-10-18 Denis Devaud , Gianluigi Rozza

The interaction between thin structures and incompressible Newtonian fluids is ubiquitous both in nature and in industrial applications. In this paper we present an isogeometric formulation of such problems which exploits a boundary…

Numerical Analysis · Mathematics 2017-02-17 Luca Heltai , Josef Kiendl , Antonio DeSimone , Alessandro Reali

The paper is concerned with locally stabilized space-time IgA approximations to initial boundary value problems of the parabolic type. Originally, similar schemes (but weighted with a global mesh parameter) was presented and studied by U.…

Numerical Analysis · Mathematics 2018-07-17 Ulrich Langer , Svetlana Matculevich , Sergey Repin

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…

Numerical Analysis · Mathematics 2018-12-27 Robert Altmann , Eric Chung , Roland Maier , Daniel Peterseim , Sai-Mang Pun

We review basic design principles underpinning the construction of mimetic finite difference and a few finite volume and finite element schemes for mixed formulations of elliptic problems. For a class of low-order mixed-hybrid schemes, we…

Numerical Analysis · Mathematics 2016-10-20 Konstantin Lipnikov , Gianmarco Manzini

In this paper, a compact and efficient code implementation is presented for isogeometric topology optimization (ITO) approach. With the aid of B\.ezier extraction technique, a derived explicit stiffness matrix computation formula is applied…

Computational Engineering, Finance, and Science · Computer Science 2025-04-14 Xianda Xie , Zhihui Ou , Aodi Yang , Xiaobing Li , Shuting Wang

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

We present an approximately $C^1$-smooth multi-patch spline construction which can be used in isogeometric analysis (IGA). A key property of IGA is that it is simple to achieve high order smoothness within a single patch. To represent more…

Numerical Analysis · Mathematics 2022-10-12 Pascal Weinmüller , Thomas Takacs

The concept of isogeometric analysis, whereby the parametric func- tions that are used to describe CAD geometry are also used to approx- imate the unknown fields in a numerical discretisation, has progressed rapidly in recent years. This…

Numerical Analysis · Mathematics 2013-02-22 R. N. Simpson , S. P. A. Bordas , H. Lian , J. Trevelyan

We present an isogeometric method for Kirchhoff-Love shell analysis of shell structures with geometries composed of multiple patches and which possibly possess extraordinary vertices, i.e. vertices with a valency different to four. The…

Numerical Analysis · Mathematics 2023-05-10 Andrea Farahat , Hugo M. Verhelst , Josef Kiendl , Mario Kapl

Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading…

Materials Science · Physics 2008-04-17 Francois Willot , Yves-Patrick Pellegrini , Pedro Ponte Castaneda

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

We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this…

Numerical Analysis · Mathematics 2021-08-04 Xiaodong Wei , Benjamin Marussig , Pablo Antolin , Annalisa Buffa

We propose two classes of mixed finite elements for linear elasticity of any order, with interior penalty for nonconforming symmetric stress approximation. One key point of our method is to introduce some appropriate nonconforming…

Numerical Analysis · Mathematics 2017-05-22 Shuonan Wu , Shihua Gong , Jinchao Xu

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

A new weak Galerkin (WG) finite element method for solving the second-order elliptic problems on polygonal meshes by using polynomials of boundary continuity is introduced and analyzed. The WG method is utilizing weak functions and their…

Numerical Analysis · Mathematics 2015-09-30 Qilong Zhai , Xiu Ye , Ruishu Wang , Ran Zhang

This paper presents a numerical method for the simulation of multiscale materials composed of an elastic matrix and slender active inclusions. The setting is motivated by the modeling of vascularized tissues and by problems arising in the…

Numerical Analysis · Mathematics 2025-08-19 Camilla Belponer , Alfonso Caiazzo , Luca Heltai

Isogeometric analysis (IGA) has emerged as a promising approach in the field of structural optimization, benefiting from the seamless integration between the computer-aided design (CAD) geometry and the analysis model by employing…

Optimization and Control · Mathematics 2024-07-02 Han Zhao , David Kamensky , John T. Hwang , Jiun-Shyan Chen

We consider the finite difference discretization of isotropic elastic wave equations on nonuniform grids. The intended applications are seismic studies, where heterogeneity of the earth media can lead to severe oversampling for simulations…

Numerical Analysis · Mathematics 2022-02-15 Longfei Gao , David Keyes