{"id":{"repo_id":"goteborg","oai_identifier":"oai:gupea.ub.gu.se:2077/52285"},"canonical_url":"https://search.dev.ndltd.org/etd/goteborg/oai:gupea.ub.gu.se:2077/52285","repository":{"repo_id":"goteborg","name":"Gothenburg University","base_url":"https://gupea.ub.gu.se/oai/request"},"display":{"title":"Efficient Adaptive Algorithms for an Electromagnetic Coefficient Inverse Problem","abstract":"This thesis comprises five scientific papers, all of which are focusing on the inverse problem of reconstructing a dielectric permittivity which may vary in space inside a given domain. The data for the reconstruction consist of time-domain observations of the electric field, resulting from a single incident wave, on a part of the boundary of the domain under consideration. The medium is assumed to be isotropic, non-magnetic, and non-conductive. We model the permittivity as a continuous function, and identify distinct objects by means of iso-surfaces at threshold values of the permittivity. Our reconstruction method is centred around the minimization of a Tikhonov functional, well known from the theory of ill-posed problems, where the minimization is performed in a Lagrangian framework inspired by optimal control theory for partial differential equations. Initial approximations for the regularization and minimization are obtained either by a so-called approximately globally convergent method, or by a (simpler but less rigorous) homogeneous background guess. The functions involved in the minimization are approximated with finite elements, or with a domain decomposition method with finite elements and finite differences. The computational meshes are refined adaptively with regard to the accuracy of the reconstructed permittivity, by means of an a posteriori error estimate derived in detail in the fourth paper. The method is tested with success on simulated as well as laboratory measured data.","abstract_html":"This thesis comprises five scientific papers, all of which are focusing on the inverse problem of reconstructing a dielectric permittivity which may vary in space inside a given domain. The data for the reconstruction consist of time-domain observations of the electric field, resulting from a single incident wave, on a part of the boundary of the domain under consideration. The medium is assumed to be isotropic, non-magnetic, and non-conductive. We model the permittivity as a continuous function, and identify distinct objects by means of iso-surfaces at threshold values of the permittivity. Our reconstruction method is centred around the minimization of a Tikhonov functional, well known from the theory of ill-posed problems, where the minimization is performed in a Lagrangian framework inspired by optimal control theory for partial differential equations. Initial approximations for the regularization and minimization are obtained either by a so-called approximately globally convergent method, or by a (simpler but less rigorous) homogeneous background guess. The functions involved in the minimization are approximated with finite elements, or with a domain decomposition method with finite elements and finite differences. The computational meshes are refined adaptively with regard to the accuracy of the reconstructed permittivity, by means of an a posteriori error estimate derived in detail in the fourth paper. The method is tested with success on simulated as well as laboratory measured data.","abstract_has_math":false,"creators":["Malmberg, John Bondestam"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-06-08","date_published":"2017-06-08","updated_at":"2026-08-21T22:21:56Z","subjects":["coefficient inverse problem","inverse scattering","Maxwell’s equations","approximate global convergence","finite element method","adaptivity,","a posteriori error analysis"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2077/52285","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"source_record":{"url":"https://gupea.ub.gu.se/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Agupea.ub.gu.se%3A2077%2F52285","prefix":"dim"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Malmberg, John Bondestam"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-06-08T11:32:56Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-06-08T11:32:56Z"]},{"key":"dc:date.issued","label":"Date","values":["2017-06-08"]},{"key":"dc:type","label":"Dc Type","values":["Text"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["coefficient inverse problem","inverse scattering","Maxwell’s equations","approximate global convergence","finite element method","adaptivity,","a posteriori error analysis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/2077/52285"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis comprises five scientific papers, all of which are focusing on the inverse problem of reconstructing a dielectric permittivity which may vary in space inside a given domain. The data for the reconstruction consist of time-domain observations of the electric field, resulting from a single incident wave, on a part of the boundary of the domain under consideration. The medium is assumed to be isotropic, non-magnetic, and non-conductive. We model the permittivity as a continuous function, and identify distinct objects by means of iso-surfaces at threshold values of the permittivity. Our reconstruction method is centred around the minimization of a Tikhonov functional, well known from the theory of ill-posed problems, where the minimization is performed in a Lagrangian framework inspired by optimal control theory for partial differential equations. Initial approximations for the regularization and minimization are obtained either by a so-called approximately globally convergent method, or by a (simpler but less rigorous) homogeneous background guess. The functions involved in the minimization are approximated with finite elements, or with a domain decomposition method with finite elements and finite differences. The computational meshes are refined adaptively with regard to the accuracy of the reconstructed permittivity, by means of an a posteriori error estimate derived in detail in the fourth paper. The method is tested with success on simulated as well as laboratory measured data."]},{"key":"dc:title","label":"Title","values":["Efficient Adaptive Algorithms for an Electromagnetic Coefficient Inverse Problem"]}]}],"canonical_facts":{"dc:creator":["Malmberg, John Bondestam"],"dc:date.accessioned":["2017-06-08T11:32:56Z"],"dc:date.available":["2017-06-08T11:32:56Z"],"dc:date.issued":["2017-06-08"],"dc:description.abstract":["This thesis comprises five scientific papers, all of which are focusing on the inverse problem of reconstructing a dielectric permittivity which may vary in space inside a given domain. The data for the reconstruction consist of time-domain observations of the electric field, resulting from a single incident wave, on a part of the boundary of the domain under consideration. The medium is assumed to be isotropic, non-magnetic, and non-conductive. We model the permittivity as a continuous function, and identify distinct objects by means of iso-surfaces at threshold values of the permittivity. Our reconstruction method is centred around the minimization of a Tikhonov functional, well known from the theory of ill-posed problems, where the minimization is performed in a Lagrangian framework inspired by optimal control theory for partial differential equations. Initial approximations for the regularization and minimization are obtained either by a so-called approximately globally convergent method, or by a (simpler but less rigorous) homogeneous background guess. The functions involved in the minimization are approximated with finite elements, or with a domain decomposition method with finite elements and finite differences. The computational meshes are refined adaptively with regard to the accuracy of the reconstructed permittivity, by means of an a posteriori error estimate derived in detail in the fourth paper. The method is tested with success on simulated as well as laboratory measured data."],"dc:identifier.uri":["http://hdl.handle.net/2077/52285"],"dc:language.iso":["eng"],"dc:subject":["coefficient inverse problem","inverse scattering","Maxwell’s equations","approximate global convergence","finite element method","adaptivity,","a posteriori error analysis"],"dc:title":["Efficient Adaptive Algorithms for an Electromagnetic Coefficient Inverse Problem"],"dc:type":["Text"]},"updated_at":"2026-08-21T22:21:56Z"}