An adaptive isogeometric boundary element method for predicting the effective thermal conductivity of steady state heterogeneity

Gong, Yanpeng; Dong, C.Y.; Qu, Xiaodong

doi:10.1016/j.advengsoft.2018.03.001

Cited by 18 publications

(6 citation statements)

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“…The adaptive integration method is based on the above formulae in conjunction with an element subdivision algorithm [49]. A full discussion of the method is beyond this paper, but a good introduction for conventional BEM can be found in [50] and its implementation in IGABEM in [2,79,80]. The key idea is the reduction of the ratios Li d by progressive subdivision of the element.…”

Section: Adaptive Integral Methods On a Surface Isogeometric Elementmentioning

confidence: 99%

“…where k = 1, 2, 3 and n k (ξ p , η p ) is the component of the unit outward normal n of the surface at x p . The values of distance d and local intrinsic coordinates ξ p and η p can be obtained by a Newton-Raphson iterative scheme as presented in [49], and more details for IGABEM implementations can be found in [79,80]. From Eq.…”

Section: Sinh Transformation Methods On a Surface Isogeometric Elementmentioning

confidence: 99%

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Hybrid nearly singular integration for three-dimensional isogeometric boundary element analysis of coatings and other thin structures

Gong

Dong

Qin

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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Section: Adaptive Integral Methods On a Surface Isogeometric Elementmentioning

confidence: 99%

Section: Sinh Transformation Methods On a Surface Isogeometric Elementmentioning

confidence: 99%

Hybrid nearly singular integration for three-dimensional isogeometric boundary element analysis of coatings and other thin structures

Gong

Dong

Qin

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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“…Based on the above analysis, and introducing an element subdivision algorithm, Gao and Davies presented the adaptive integration method in [53,54], giving details of the derivation and implementation for the conventional BEM. The implementation of the adaptive integral method in IGABEM can be found in [80,81].…”

Section: Adaptive Integral Methodsmentioning

confidence: 99%

“…The method is also used in the adaptive integral method for computing the minimum distance from source point to sub-element. More details about the Newton-Raphson method for the conventional BEM can be found in [53], and the application for IGABEM has been given in [81].…”

Section: Sinh Transformation Methodsmentioning

confidence: 99%

Hybrid nearly singular integration for isogeometric boundary element analysis of coatings and other thin 2D structures

Gong

Trevelyan

Hattori

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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We present an isogeometric boundary element method (IGABEM) capable of delivering accurate and efficient solutions in the heat transfer analysis of 2D coated structures such as those commonly found in turbomachinery. Although we consider very thin coatings (of thickness down to 10 −7 m), they are modelled explicitly as BEM zones, and this is made possible by the development of a new integration scheme (sinh +) aimed particularly at the challenging nearly singular integrals that arise. Sinh + is a hybrid of adaptive and sinh transformation approaches, and we make further extensions to the latter to improve its robustness. The scheme is tuned to deliver results of engineering accuracy in an optimal time. The scheme is adaptable, by changing a tolerance, to enable engineers to achieve a different balance between accuracy and computational efficiency as may be required for different applications. A set of numerical examples demonstrates the ability of the scheme to produce accurate temperature distributions efficiently in the presence of very thin coatings.

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“…The quadrature rule from Telles (1987) is combined with Gauss-Legendre quadrature for linear elastic problems considering homogeneous material (Karam and Telles, 1988;Simpson et al, 2012) and liquid inclusions (Dai et al, 2021) and for FSI problems considering Stokes Flow (Patiño and Nieto-Londoño, 2021). The adaptive integral method for near singular integrals (Gao and Davies, 2000) is used to solve Laplace's equation by isogeometric BE analysis for potential problems (Gong and Dong, 2017), thermal problems (Gong et al, 2018) and thermoelasticity problems (Gong et al, 2020), whereas the singularity subtraction method (Guiggiani et al, 1992) is applied in Jarvenpaa et al (2006) to electromagnetics and in Peng et al (2017) to fracture mechanics. Ata and Sahin (2018) consider the tanh-sinh quadrature rule (Borwein and Ye, 2006) for BE analysis of Stokes flow problems and Keuchel et al (2017) apply the sinhquadrature (Johnston et al, 2007) to nearly singular integrals in the Burton-Miller formulation of the Helmholtz equation for acoustic problems.…”

Section: Application To Be Analysismentioning

confidence: 99%

New hybrid quadrature schemes for weakly singular kernels applied to isogeometric boundary elements for 3D Stokes flow

Harmel¹,

Sauer²

2022

Preprint

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This work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for several partial differential equations including the Stokes equation for viscous flow and the Helmholtz equation for acoustics. The proposed quadrature schemes apply a Duffy transform-based quadrature rule (Duffy, 1982) to surface elements containing the singularity and classical Gaussian quadrature to the remaining elements. Two of the four schemes additionally consider a special treatment for elements near to the singularity, where refined Gaussian quadrature and a new moment-fitting quadrature rule are used. The hybrid quadrature schemes are systematically studied on flat B-spline patches and on NURBS spheres considering two different sphere discretizations: An exact single-patch sphere with degenerate control points at the poles and an approximate discretization that consist of six patches with regular elements. The efficiency of the quadrature schemes is further demonstrated in boundary element analysis for Stokes flow, where steady problems with rotating and translating curved objects are investigated in convergence studies for both, mesh and quadrature refinement. Much higher convergence rates are observed for the proposed new schemes in comparison to classical schemes.

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An adaptive isogeometric boundary element method for predicting the effective thermal conductivity of steady state heterogeneity

Cited by 18 publications

References 50 publications

Hybrid nearly singular integration for three-dimensional isogeometric boundary element analysis of coatings and other thin structures

Hybrid nearly singular integration for three-dimensional isogeometric boundary element analysis of coatings and other thin structures

Hybrid nearly singular integration for isogeometric boundary element analysis of coatings and other thin 2D structures

New hybrid quadrature schemes for weakly singular kernels applied to isogeometric boundary elements for 3D Stokes flow

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