Show simple item record

dc.contributor.authorAlexe, Mihaien_US
dc.date.accessioned2014-03-14T21:10:09Z
dc.date.available2014-03-14T21:10:09Z
dc.date.issued2011-03-18en_US
dc.identifier.otheretd-03292011-175733en_US
dc.identifier.urihttp://hdl.handle.net/10919/37515
dc.description.abstractAdaptivity in both space and time has become the norm for solving problems modeled by partial differential equations. The size of the discretized problem makes uniformly refined grids computationally prohibitive. Adaptive refinement of meshes and time steps allows to capture the phenomena of interest while keeping the cost of a simulation tractable on the current hardware. Many fields in science and engineering require the solution of inverse problems where parameters for a given model are estimated based on available measurement information. In contrast to forward (regular) simulations, inverse problems have not extensively benefited from the adaptive solver technology. Previous research in inverse problems has focused mainly on the continuous approach to calculate sensitivities, and has typically employed fixed time and space meshes in the solution process. Inverse problem solvers that make exclusive use of uniform or static meshes avoid complications such as the differentiation of mesh motion equations, or inconsistencies in the sensitivity equations between subdomains with different refinement levels. However, this comes at the cost of low computational efficiency. More efficient computations are possible through judicious use of adaptive mesh refinement, adaptive time steps, and the discrete adjoint method. This dissertation develops a complete framework for fully discrete adjoint sensitivity analysis and inverse problem solutions, in the context of time dependent, adaptive mesh, and adaptive step models. The discrete framework addresses all the necessary ingredients of a stateâ ofâ theâ art adaptive inverse solution algorithm: adaptive mesh and time step refinement, solution grid transfer operators, a priori and a posteriori error analysis and estimation, and discrete adjoints for sensitivity analysis of fluxâ limited numerical algorithms.en_US
dc.publisherVirginia Techen_US
dc.relation.haspartAlexe_M_D_2011.pdfen_US
dc.rightsI hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Virginia Tech or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.en_US
dc.subjectInverse problemsen_US
dc.subjectAdjoint Methoden_US
dc.subjectAdaptive Mesh Refinementen_US
dc.subjectAutomatic Differentiationen_US
dc.titleAdjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problemsen_US
dc.typeDissertationen_US
dc.contributor.departmentComputer Scienceen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineComputer Scienceen_US
dc.contributor.committeechairSandu, Adrianen_US
dc.contributor.committeememberRibbens, Calvin J.en_US
dc.contributor.committeememberCao, Yangen_US
dc.contributor.committeememberDe Sturler, Ericen_US
dc.contributor.committeememberBorggaard, Jeffrey T.en_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-03292011-175733/en_US
dc.date.sdate2011-03-29en_US
dc.date.rdate2011-04-14
dc.date.adate2011-04-14en_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record