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dc.contributor.advisorLaleg-Kirati, Taous-Meriem
dc.contributor.authorMajeed, Muhammad Usman
dc.date.accessioned2017-07-20T08:58:18Z
dc.date.available2017-07-20T08:58:18Z
dc.date.issued2017-07-19
dc.identifier.doi10.25781/KAUST-90472
dc.identifier.urihttp://hdl.handle.net/10754/625240
dc.descriptionA recording of the defense presentation for this dissertation is available at: http://hdl.handle.net/10754/625197
dc.description.abstractSteady-state elliptic partial differential equations (PDEs) are frequently used to model a diverse range of physical phenomena. The source and boundary data estimation problems for such PDE systems are of prime interest in various engineering disciplines including biomedical engineering, mechanics of materials and earth sciences. Almost all existing solution strategies for such problems can be broadly classified as optimization-based techniques, which are computationally heavy especially when the problems are formulated on higher dimensional space domains. However, in this dissertation, feedback based state estimation algorithms, known as state observers, are developed to solve such steady-state problems using one of the space variables as time-like. In this regard, first, an iterative observer algorithm is developed that sweeps over regular-shaped domains and solves boundary estimation problems for steady-state Laplace equation. It is well-known that source and boundary estimation problems for the elliptic PDEs are highly sensitive to noise in the data. For this, an optimal iterative observer algorithm, which is a robust counterpart of the iterative observer, is presented to tackle the ill-posedness due to noise. The iterative observer algorithm and the optimal iterative algorithm are then used to solve source localization and estimation problems for Poisson equation for noise-free and noisy data cases respectively. Next, a divide and conquer approach is developed for three-dimensional domains with two congruent parallel surfaces to solve the boundary and the source data estimation problems for the steady-state Laplace and Poisson kind of systems respectively. Theoretical results are shown using a functional analysis framework, and consistent numerical simulation results are presented for several test cases using finite difference discretization schemes.
dc.language.isoen
dc.relation.urlhttp://hdl.handle.net/10754/625197
dc.subjectobserver design
dc.subjectInverse problems
dc.subjectBoundary Estimation
dc.subjectsource localization
dc.subjectelliptic PDEs
dc.subjectkalman filter
dc.titleIterative Observer-based Estimation Algorithms for Steady-State Elliptic Partial Differential Equation Systems
dc.typeDissertation
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
thesis.degree.grantorKing Abdullah University of Science and Technology
dc.contributor.committeememberShamma, Jeff S.
dc.contributor.committeememberKeyes, David E.
dc.contributor.committeememberWu, Ying
dc.contributor.committeememberSmith, Ralph
thesis.degree.disciplineApplied Mathematics and Computational Science
thesis.degree.nameDoctor of Philosophy
refterms.dateFOA2018-06-14T05:24:56Z


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