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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/3369

Title: Mesh-based numerical implementation of the localized boundary-domain integral equation method to a variable-coefficient Neumann problem
Authors: Mikhailov, SE
Nakhova, IS
Keywords: Cut-off function
Finite-dimensional perturbation
Integral equation
Linear partial differential equation
Localized parametrix
Sparse matrix
Publication Date: 2005
Publisher: Springer
Citation: Journal of Engineering Mathematics. 51(3): 251-259, Mar 2005
Abstract: An implementation of the localized boundary-domain integral-equation (LBDIE) method for the numerical solution of the Neumann boundary-value problem for a second-order linear elliptic PDE with variable coefficient is discussed. The LBDIE method uses a specially constructed localized parametrix (Levi function) to reduce the BVP to a LBDIE. After employing a mesh-based discretization, the integral equation is reduced to a sparse system of linear algebraic equations that is solved numerically. Since the Neumann BVP is not unconditionally and uniquely solvable, neither is the LBDIE. Numerical implementation of the finite-dimensional perturbation approach that reduces the integral equation to an unconditionally and uniquely solvable equation, is also discussed.
URI: http://www.springerlink.com/content/kw59137483183940/?p=74d83dbf32294166b802e9ad69f0a1ad&pi=1
http://bura.brunel.ac.uk/handle/2438/3369
Appears in Collections:Mathematics
School of Information Systems, Computing and Mathematics Research Papers

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