Boundary Element Techniques

Brebbia, Carlos Alberto; Telles, J. C. F.; Wrobel, L.C.

doi:10.1007/978-3-642-48860-3

Cited by 2,441 publications

(843 citation statements)

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“…This formulation will be used in the sequel to derive the two standard approximation approaches in BEM practice, namely the Galerkin and the collocation method, [Brebbia et al 1984]. For this purpose, we rewrite (22) as…”

Section: The Isogeometric-bem Conceptmentioning

confidence: 99%

“…Some of the most important advantages of this approach are: i) reduction of the dimensionality of the problem by one, facilitating calculations around complex geometrical configurations (especially in 3-D problems) and ii) consistent treatment of conditions at infinity. As regards the numerical solution of the integral equations, Boundary Element Methods (BEM) serve today as the main tool, [Hess 1975], [Brebbia et al 1984], [Paris and Canas 1997], [Brebbia 2002], although various other techniques are also available, such as spectral methods using basis functions of global support on the boundary surface.…”

Section: Introductionmentioning

confidence: 99%

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An isogeometric BEM for exterior potential-flow problems in the plane

Politis

Ginnis²,

Kaklis³

et al. 2009

2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling

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Section: The Isogeometric-bem Conceptmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An isogeometric BEM for exterior potential-flow problems in the plane

Politis

Ginnis²,

Kaklis³

et al. 2009

2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling

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“…For further details regarding this key treatment of the integral in (3.10), the reader is directed to standard textbooks (see Brebbia, Telles & Wrobel 1984;Bonnet 1995) and also to Sellier (2010). The discretized counterpart of (3.10) then becomes a linear system A · X = B, with the 3N-dimensional unknown discretized density vector X and a 3N × 3N square, dense, non-symmetric so-called influence matrix A.…”

Section: Determination Of the Green's Tensormentioning

confidence: 99%

Motion of a solid particle in a shear flow along a porous slab

et al. 2012

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The flow field around a solid particle moving in a shear flow along a porous slab is obtained by solving the coupled Stokes-Darcy problem with the Beavers and Joseph slip boundary condition on the slab interfaces. The solution involves the Green's function of this coupled problem, which is given here. It is shown that the classical boundary integral method using this Green's function is inappropriate because of supplementary contributions due to the slip on the slab interfaces. An 'indirect boundary integral method' is therefore proposed, in which the unknown density on the particle surface is not the actual stress, but yet allows calculation of the force and torque on the particle. Various results are provided for the normalized force and torque, namely friction factors, on the particle. The cases of a sphere and an ellipsoid are considered. It is shown that the relationships between friction coefficients (torque due to rotation and force due to translation) that are classical for a no-slip plane do not apply here. This difference is exhibited. Finally, results for the velocity of a freely moving particle in a linear and a quadratic shear flow are presented, for both a sphere and an ellipsoid.

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“…The boundary-value problern for modeling area Ieads to the following boundary integral equations [9].…”

Section: Problem Formulation and Solutionmentioning

confidence: 99%