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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 |
Issue 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: | Dept of Mathematics Research Papers Mathematical Sciences |
Files in This Item:
File | Description | Size | Format | |
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Mesh-based numerical implementation.pdf | 459.12 kB | Adobe PDF | View/Open |
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