Domain decomposition boundary element method with overlapping sub-domains

Thanh, Tung Bui; Popov, Viktor

doi:10.1016/j.enganabound.2008.09.002

Cited by 22 publications

(13 citation statements)

References 19 publications

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“…This problem could be overcome either increasing the numerical precision or improving the linear solver. It is fair to mention that similar improvement on the solution can be achieved with the RBIEM scheme by using more than one integration point for sub-domain instead of only one as original proposed in [9].…”

Section: Numerical Resultsmentioning

confidence: 74%

“…Popov and [8] introduced the radial basis integral equation method (RBIEM). It naturally extends from the work of Popov and Bui [9] by adopting circular subdomains and by using interpolation to obtain the distributions over the local boundaries. The RBIEM evaluates the derivatives by employing two in 2D problems additional equations obtained by differentiating the local integral equation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Local regular dual reciprocity method for 2D convection-diffusion equation

Caruso¹,

Portapila²,

Power³

2012

WIT Transactions on Modelling and Simulation

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In this paper a new technique considering the dual reciprocity method (DRM) with only internal collocation points is considered along with local radial basis function interpolation. This approach gives rise to regular integral equations. Numerical results for the convection-diffusion equation are presented for different Peclet numbers. Comparisons with other numerical techniques are shown in order to illustrate the good solutions obtained by this method.

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Section: Numerical Resultsmentioning

confidence: 74%

Section: Introductionmentioning

confidence: 99%

Local regular dual reciprocity method for 2D convection-diffusion equation

Caruso¹,

Portapila²,

Power³

2012

WIT Transactions on Modelling and Simulation

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“…Alternatively, it is possible in some numerical techniques to impose the complete set of matching conditions by defining an over-determined system of equations which can be solved in a least square sense with the associated approximation error, see for example the DRM-MD technique of Popov and Power [37]. More recently Bui and Popov [4] introduced an overlapping domain decomposition technique valid for any BEM formulation, in order to obtain a system of equations that is always closed.…”

Section: Steady State Heat Transfer Problem In a Circular Cylinder Wimentioning

confidence: 99%

The Hermite radial basis function control volume method for multi-zones problems; A non-overlapping domain decomposition algorithm

Orsini

Power

Lees

2011

Computer Methods in Applied Mechanics and Engineering

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“…Similarly to the LBIE it is implemented over circular sub-domains where the source points are placed in the centres of the circles. The work follows the idea of Bui and Popov [4] who proposed using three equations at each source point for 2D problems solved using BEM with overlapping sub-domains. One equation is the original integral equation usually used in the direct formulation BEM, while the other two equations are the derivatives in respect to spatial coordinates of the original equation at the source point.…”

Section: Introductionmentioning

confidence: 99%