Numerical solution and spectrum of boundary-domain integral equations

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.

Grantor dc:publisher

Brunel University, School of Information Systems, Computing and Mathematics

Year dc:date.issued

2013

Author dc:creator

• Mohamed, Nurul Akmal

Advisor dc:contributor.advisor

• Mikhailov, SE

• Localised boundary-domain integral equation
• Spectrum
• Neumann series
• Bilinear interpolation
• Semi-analytic method

Language dc:language.iso

en

Repository record dc:identifier.uri

http://bura.brunel.ac.uk/handle/2438/7592

OAI identifier oai:identifier

oai:bura.brunel.ac.uk:2438/7592