Isogeometric Boundary Element analysis with elasto-plastic inclusions. Part 2: 3-D problems

Beer, Gernot; Marussig, Benjamin; Zechner, Jürgen; Dünser, Christian; Fries, Thomas‐Peter

doi:10.1016/j.cma.2016.11.007

Cited by 38 publications

(15 citation statements)

References 11 publications

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“…For some problems, this issue can be overcome by the use of boundary element methods. Indeed, many applications of isogeometric boundary element methods have been introduced in recent years [2,22,23,32,42,43]. These go beyond the scope of academic examples and show that isogeometric boundary methods are ready for industrial application.…”

Section: Introductionmentioning

confidence: 99%

Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis

et al. 2019

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We define a conforming B-spline discretisation of the de Rham complex on multipatch geometries. We introduce and analyse the properties of interpolation operators onto these spaces which commute w.r.t. the surface differential operators. Using these results as a basis, we derive new convergence results of optimal order w.r.t. the respective energy spaces and provide approximation properties of the spline discretisations of trace spaces for application in the theory of isogeometric boundary element methods. Our analysis allows for a straight forward generalisation to finite element methods.

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Section: Introductionmentioning

confidence: 99%

Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis

et al. 2019

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“…Indeed, isogeometric boundary element methods have recently been tested successfully for multiple engineering applications, see e.g. [2,25,33,34].…”

Section: Introductionmentioning

confidence: 99%

A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems

Dölz

Harbrecht

Kurz

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract the problems arising due to the dense matrices produced by boundary element methods. By solving Laplace and Helmholtz problems via a single layer approach we show, through a series of numerical examples suitable for easy comparison with other numerical schemes, that one can indeed achieve extremely high rates of convergence of the pointwise potential through the utilisation of higher order B-spline-based ansatz functions.

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“…We base our work on the developments made by the team of Gernot Beer in two important papers for isogeometric boundary element methods: [7,33], which were further developed in a series of papers targeting geomechanics problems [6,4,8,7,34,69,5].…”

Section: Contributionmentioning

confidence: 99%

“…where J −T (ξ) is the transpose of the inverse of the Jacobian matrix (5). Now let the weak form of the boundary value problem be given by…”

Section: Formulation Of Giftmentioning

confidence: 99%

“…Although the finite element version of IGA suffers from significant difficulties associated with generating volumetric parameterisations directly from CAD, coupling IGA with boundary element methods enables to perform computations directly from the CAD description of the boundary of the domain [3]. Applications include stress analysis [58,32,51], shape optimization [54,31,30], fracture mechanics [44,45,43,46], geomechanics [6,33,4,8,7,34,69,5], acoustics [59,27], and electromagnetics [13]. A detailed overview of the recent work in the field can be found in [39] and in [29].…”

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confidence: 99%

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Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub‐ and super‐geometric analysis to Geometry‐Independent Field approximaTion (GIFT)

Atroshchenko

Tomar

et al. 2018

Numerical Meth Engineering

102

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This paper presents an approach to generalize the concept of isogeometric analysis by allowing different spaces for the parameterization of the computational domain and for the approximation of the solution field. The method inherits the main advantage of isogeometric analysis, ie, preserves the original exact computer-aided design geometry (for example, given by nonuniform rational B-splines), but allows pairing it with an approximation space, which is more suitable/flexible for analysis, for example, T-splines, LR-splines, (truncated) hierarchical B-splines, and PHT-splines. This generalization offers the advantage of adaptive local refinement without the need to reparameterize the domain, and therefore without weakening the link with the computer-aided design model. We demonstrate the use of the method with different choices of geometry and field spaces and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for nonnested spaces.

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Isogeometric Boundary Element analysis with elasto-plastic inclusions. Part 2: 3-D problems

Cited by 38 publications

References 11 publications

Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis

Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis

A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems

Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub‐ and super‐geometric analysis to Geometry‐Independent Field approximaTion (GIFT)

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