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http://bura.brunel.ac.uk/handle/2438/7592
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. |
URI: | http://bura.brunel.ac.uk/handle/2438/7592 |
Appears in Collections: | Brunel University Theses Dept of Mathematics Theses Mathematical Sciences |
Files in This Item:
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FulltextThesis.pdf | 860.53 kB | Adobe PDF | View/Open |
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