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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:575680 |
| Date | January 2013 |
| Creators | Mohamed, Nurul Akmal |
| Contributors | Mikhailov, S. E. |
| Publisher | Brunel University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://bura.brunel.ac.uk/handle/2438/7592 |
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