{"id":{"repo_id":"brunel","oai_identifier":"oai:bura.brunel.ac.uk:2438/7592"},"canonical_url":"https://search.dev.ndltd.org/etd/brunel/oai:bura.brunel.ac.uk:2438/7592","repository":{"repo_id":"brunel","name":"University of Brunel","base_url":"https://bura.brunel.ac.uk/oai/request"},"display":{"title":"Numerical solution and spectrum of boundary-domain integral equations","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Mohamed, Nurul Akmal"],"institution":"Brunel University, School of Information Systems, Computing and Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Mikhailov, SE"],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013","date_published":"2013","updated_at":"2026-07-24T01:23:28Z","subjects":["Localised boundary-domain integral equation","Spectrum","Neumann series","Bilinear interpolation","Semi-analytic method"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://bura.brunel.ac.uk/handle/2438/7592","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Mikhailov, SE"]},{"key":"dc:creator","label":"Author","values":["Mohamed, Nurul Akmal"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2013-07-12T13:32:45Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-07-12T13:32:45Z"]},{"key":"dc:date.issued","label":"Date","values":["2013"]},{"key":"dc:publisher","label":"Institution","values":["Brunel University, School of Information Systems, Computing and Mathematics"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Localised boundary-domain integral equation","Spectrum","Neumann series","Bilinear interpolation","Semi-analytic method"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://bura.brunel.ac.uk/handle/2438/7592"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Numerical solution and spectrum of boundary-domain integral equations"]}]}],"canonical_facts":{"dc:contributor.advisor":["Mikhailov, SE"],"dc:creator":["Mohamed, Nurul Akmal"],"dc:date.accessioned":["2013-07-12T13:32:45Z"],"dc:date.available":["2013-07-12T13:32:45Z"],"dc:date.issued":["2013"],"dc:description":["This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University."],"dc:description.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."],"dc:identifier.uri":["http://bura.brunel.ac.uk/handle/2438/7592"],"dc:language.iso":["en"],"dc:publisher":["Brunel University, School of Information Systems, Computing and Mathematics"],"dc:subject":["Localised boundary-domain integral equation","Spectrum","Neumann series","Bilinear interpolation","Semi-analytic method"],"dc:title":["Numerical solution and spectrum of boundary-domain integral equations"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T01:23:28Z"}