Isogeometric symmetric Galerkin boundary element method for three-dimensional elasticity problems

Nguyen, Bang Van; Zhuang, Xiaoying; Wriggers, Peter; Rabczuk, Timon; Mear, Mark E.; Tran, Han D.

doi:10.1016/j.cma.2017.05.011

Cited by 29 publications

(6 citation statements)

References 25 publications

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“…The potential benefits of using IGA for the solution of boundary integral equations were already mentioned in the conclusions of [ 129 ], but it has only been considered first in [ 178 ]. The research on IGABEM has steadily grown since then, although not as fast as for IGAFEM, with applications in acoustics [ 61 , 82 , 196 , 205 ], elasticity [ 13 , 168 ], electromagnetics [ 83 , 195 , 204 ], lifting flow [ 63 ], potential flow [ 118 , 140 , 141 ], and solid mechanics [ 156 , 190 ], see also the recent book [ 17 ] for a comprehensive survey of the topic and a complete review of the existing literature. An implementation of (non-adaptive) IGABEM is available in the open-source library Bembel [ 81 ].…”

Section: Model Problems and Isogeometric Analysismentioning

confidence: 99%

Mathematical Foundations of Adaptive Isogeometric Analysis

Buffa

Gantner

Giannelli

et al. 2022

Arch Computat Methods Eng

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This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the local resolution of possible singularities as well as the state-of-the-art formulation of convergence and quasi-optimality of adaptive algorithms for both the finite element method and the boundary element method in the frame of isogeometric analysis.

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Section: Model Problems and Isogeometric Analysismentioning

confidence: 99%

Mathematical Foundations of Adaptive Isogeometric Analysis

Buffa

Gantner

Giannelli

et al. 2022

Arch Computat Methods Eng

View full text Add to dashboard Cite

show abstract

“…The potential benefits of using IGA for the solution of boundary integral equations were already mentioned in the conclusions of [123], but it has only been considered first in [172]. The research on IGABEM has steadily grown since then, although not as fast as for IGAFEM, with applications in acoustics [189,76,61,198], elasticity [13,162], electromagnetics [197,188,77], lifting flow [63], potential flow [112,134,135], and solid mechanics [183,150], see also the recent book [17] for a comprehensive survey of the topic and a complete review of the existing literature. An implementation of (non-adaptive) IGABEM is available in the open-source library Bembel [75].…”

Section: Isogeometric Analysis For Bem (Igabem)mentioning

confidence: 99%

Mathematical Foundations of Isogeometric Analysis

et al. 2020

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isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the local resolution of possible singularities as well as the state-of-the-art formulation of convergence and quasi-optimality of adaptive algorithms for both the finite element method (FEM) and the boundary element method (BEM) in the frame of isogeometric analysis (IGA).

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“…Three dimensional problems need trivariate NURBS solids for analysis, but CAD systems use a boundary representation where only bivariate NURBS are involved. A possible solution to this issue consists in adopting boundary element methods (BEMs) [6,26], whose isogeometric formulation is briefly referred to as IGA-BEM and has recently been succesfully applied to several classical problems, e.g., Laplace and Helmholtz equation [29,14], elastostatics and elasticity [27,31,5,24], potential flow [18] and wave-resistance problems [17]. BEMs reformulate the original differential problem through the fundamental solution into boundary integral equations.…”

Section: Introductionmentioning

confidence: 99%

A collocation IGA-BEM for 3D potential problems on unbounded domains

Falini,

Giannelli,

Kanduc

et al. 2022

Preprint

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In this paper the numerical solution of potential problems defined on 3D unbounded domains is addressed with Boundary Element Methods (BEMs), since in this way the problem is studied only on the boundary, and thus any finite approximation of the infinite domain can be avoided. The isogeometric analysis (IGA) setting is considered and in particular B-splines and NURBS functions are taken into account. In order to exploit all the possible benefits from using spline spaces, an important point is the development of specific cubature formulas for weakly and nearly singular integrals. Our proposal for this aim is based on spline quasi-interpolation and on the use of a spline product formula. Besides that, a robust singularity extraction procedure is introduced as a preliminary step and an efficient function-byfunction assembly phase is adopted. A selection of numerical examples confirms that the numerical solutions reach the expected convergence orders.

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Isogeometric symmetric Galerkin boundary element method for three-dimensional elasticity problems

Cited by 29 publications

References 25 publications

Mathematical Foundations of Adaptive Isogeometric Analysis

Mathematical Foundations of Adaptive Isogeometric Analysis

Mathematical Foundations of Isogeometric Analysis

A collocation IGA-BEM for 3D potential problems on unbounded domains

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