Resistor Network Approaches to the Numerical Solution of Electrical Impedance Tomography with Partial Boundary Measurements

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dc.contributor.advisorBorcea, Lilianaen_US
dc.creatorMamonov, Alexander Vasilyevicen_US
dc.date.accessioned2018-11-26T17:15:17Zen_US
dc.date.available2018-11-26T17:15:17Zen_US
dc.date.issued2009en_US
dc.description.abstractElectrical Impedance Tomography (EIT) problem consists of finding the electric conductivity inside a conductive body from simultaneous measurements of electric potential and current at its boundary. The EIT problem with partial boundary measurements corresponds to the case, where only certain portions of the boundary are available for measuring the potentials and currents. A deep connection exists between the EIT problem in continuum and the discrete inverse problem of recovering the conductances of resistors in a resistor network. The connection comes in the form of special finite volume discretizations on carefully chosen grids, known as optimal grids. The optimal grids allows us to use the existing theory of inverse problems for resistor networks to compute an approximation to the solution of the continuum EIT problem. This was done recently in the case of full boundary measurements. The main goal of our work is to generalize the existing results to the case of partial measurement settings. Two alternative approaches are presented: one is based on (quasi-) conformal mappings of a well-studied conductivity problem in a unit disk, and the other is based on a previously unstudied pyramidal graph topology. We establish the existence and uniqueness of the solutions of discrete problems for both settings. Then we use these discrete results to obtain numerical approximations to the solution of the continuum EIT problem with partial measurements.en_US
dc.format.digitalOriginreformatted digitalen_US
dc.format.extent93 ppen_US
dc.identifier.callnoTHESIS MATH.SCI. 2010 MAMONOVen_US
dc.identifier.citationMamonov, Alexander Vasilyevic. "Resistor Network Approaches to the Numerical Solution of Electrical Impedance Tomography with Partial Boundary Measurements." (2009) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/103411">https://hdl.handle.net/1911/103411</a>.en_US
dc.identifier.digitalRICE2558en_US
dc.identifier.urihttps://hdl.handle.net/1911/103411en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectApplied Mathematicsen_US
dc.subjectMathematicsen_US
dc.subjectApplied sciencesen_US
dc.subjectPure sciencesen_US
dc.titleResistor Network Approaches to the Numerical Solution of Electrical Impedance Tomography with Partial Boundary Measurementsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.majorComputational and Applied Mathematicsen_US
thesis.degree.nameMaster of Artsen_US
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