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Title: Numerical solution and spectrum of boundary-domain integral equations
Authors: Mohamed, Nurul Akmal
Advisors: Mikhailov, SE
Keywords: Localised boundary-domain integral equation;Spectrum;Neumann series;Bilinear interpolation;Semi-analytic method
Issue Date: 2013
Publisher: Brunel University, School of Information Systems, Computing and Mathematics
Abstract: A numerical implementation of the direct Boundary-Domain Integral Equation (BDIE)/ Boundary-Domain Integro-Differential Equations (BDIDEs) and Localized Boundary-Domain Integral Equation (LBDIE)/Localized Boundary-Domain Integro-Differential Equations (LBDIDEs) related to the Neumann and Dirichlet boundary value problem for a scalar elliptic PDE with variable coefficient is discussed in this thesis. The BDIE and LBDIE related to Neumann problem are reduced to a uniquely solvable one by adding an appropriate perturbation operator. The mesh-based discretisation of the BDIE/BDIDEs and LBDIE/LBDIDEs with quadrilateral domain elements leads to systems of linear algebraic equations (discretised BDIE/BDIDEs/LBDIE/BDIDEs). Then the systems obtained from BDIE/BDIDE (discretised BDIE/BDIDE) are solved by the LU decomposition method and Neumann iterations. Convergence of the iterative method is analyzed in relation with the eigen-values of the corresponding discrete BDIE/BDIDE operators obtained numerically. The systems obtained from LBDIE/LBDIDE (discretised LBDIE/LBDIDE) are solved by the LU decomposition method as the Neumann iteration method diverges.
Description: This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.
Appears in Collections:Brunel University Theses
Dept of Mathematics Theses
Mathematical Sciences

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