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Three-dimensional solution for acoustic and transport problems using the radial basis integral equation method

Three-dimensional solution for acoustic and transport problems using the radial basis integral equation method
Three-dimensional solution for acoustic and transport problems using the radial basis integral equation method
The radial basis integral equations method (RBIEM) has been applied for solution of three-dimensional (3D) acoustic and transport problems. The acoustic problem is often described using the Helmholtz equation, while the transport problems are usually described using the Laplace equation (diffusion only), the Poisson equation (diffusion with sources/sinks) and the convection–diffusion equation. The accuracy of the numerical scheme employing the first and second order Duchon splines augmented by first and second order polynomials, respectively, was examined. The effect of the number of interpolation points used in the radial basis function approximation on the condition number of the system was investigated. Numerical results obtained for the convection–diffusion equation were compared with the solutions obtained using the multi-domain dual reciprocity boundary element method (DRM-MD). The RBIEM formulation was found to be more accurate than the DRM-MD formulation. The implementation does not involve discretization over the boundaries of the subdomains used in the RBIEM formulation when evaluating the integrals
0096-3003
9470-9488
Ooi, E.H.
ff48a294-3f9b-4f98-8fdd-2da2f28247ba
Popov, V.
0554231d-ba93-4f53-a2d6-c8b2de1bb2bd
Dogan, H.
a1e136a9-aab8-4942-a977-0ae3440758cc
Ooi, E.H.
ff48a294-3f9b-4f98-8fdd-2da2f28247ba
Popov, V.
0554231d-ba93-4f53-a2d6-c8b2de1bb2bd
Dogan, H.
a1e136a9-aab8-4942-a977-0ae3440758cc

Ooi, E.H., Popov, V. and Dogan, H. (2012) Three-dimensional solution for acoustic and transport problems using the radial basis integral equation method. Applied Mathematics and Computation, 218 (18), 9470-9488. (doi:10.1016/j.amc.2012.03.037).

Record type: Article

Abstract

The radial basis integral equations method (RBIEM) has been applied for solution of three-dimensional (3D) acoustic and transport problems. The acoustic problem is often described using the Helmholtz equation, while the transport problems are usually described using the Laplace equation (diffusion only), the Poisson equation (diffusion with sources/sinks) and the convection–diffusion equation. The accuracy of the numerical scheme employing the first and second order Duchon splines augmented by first and second order polynomials, respectively, was examined. The effect of the number of interpolation points used in the radial basis function approximation on the condition number of the system was investigated. Numerical results obtained for the convection–diffusion equation were compared with the solutions obtained using the multi-domain dual reciprocity boundary element method (DRM-MD). The RBIEM formulation was found to be more accurate than the DRM-MD formulation. The implementation does not involve discretization over the boundaries of the subdomains used in the RBIEM formulation when evaluating the integrals

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Published date: 30 March 2012
Organisations: Inst. Sound & Vibration Research

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Local EPrints ID: 376829
URI: http://eprints.soton.ac.uk/id/eprint/376829
ISSN: 0096-3003
PURE UUID: fd000a49-c6fd-40dd-8894-aaadeba4c178

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Date deposited: 07 May 2015 09:14
Last modified: 14 Mar 2024 19:50

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Contributors

Author: E.H. Ooi
Author: V. Popov
Author: H. Dogan

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