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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.
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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