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Title: Boundary element formulations for the numerical solution of two-dimensional diffusion problems with variable coefficients
Authors: Al-Jawary, MA
Ravnik, J
Wrobel, LC
Škerget, L
Keywords: Boundary element method;Variable coefficient;Boundary-domain integral equation;Boundary-domain integro-differential equation;Radial integration method;Domain decomposition
Issue Date: 2012
Publisher: Elsevier
Citation: Computers & Mathematics with Applications, 64(8), 2695 - 2711, 2012
Abstract: This paper presents new formulations of the radial integration boundary integral equation (RIBIE) and the radial integration boundary integro-differential equation (RIBIDE) methods for the numerical solution of two-dimensional diffusion problems with variable coefficients. The methods use either a specially constructed parametrix (Levi function) or the standard fundamental solution for the Laplace equation to reduce the boundary-value problem (BVP) to a boundary–domain integral equation (BDIE) or boundary–domain integro-differential equation (BDIDE). The radial integration method (RIM) is then employed to convert the domain integrals arising in both BDIE and BDIDE methods into equivalent boundary integrals. The resulting formulations lead to pure boundary integral and integro-differential equations with no domain integrals. Furthermore, a subdomain decomposition technique (SDBDIE) is proposed, which leads to a sparse system of linear equations, thus avoiding the need to calculate a large number of domain integrals. Numerical examples are presented for several simple problems, for which exact solutions are available, to demonstrate the efficiency of the proposed approaches.
Description: This is the post-print version of the final paper published in Computers & Mathematics with Applications. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2012 Elsevier B.V.
ISSN: 0898-1221
Appears in Collections:Mechanical and Aerospace Engineering
Dept of Mechanical Aerospace and Civil Engineering Research Papers

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