Accelerated PDE Constrained Optimization using Direct Solvers

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dc.contributor.advisorGillman, Adriannaen_US
dc.contributor.committeeMemberHeinkenschloss, Matthiasen_US
dc.creatorGeldermans, Peteren_US
dc.date.accessioned2019-05-16T20:12:09Zen_US
dc.date.available2019-05-16T20:12:09Zen_US
dc.date.created2018-05en_US
dc.date.issued2018-04-17en_US
dc.date.submittedMay 2018en_US
dc.date.updated2019-05-16T20:12:09Zen_US
dc.description.abstractIn this thesis, I propose a method to reduce the cost of computing solutions to optimization problems governed by partial differential equations (PDEs). Standard second order methods such as Newton require the solution of two PDEs per iteration of the Newton system, which can be prohibitively expensive for iterative solvers. In contrast, this work takes advantage a recently developed high order discretization method that comes with an efficient direct solver. The new technique precomputes a solution operator that can be reused for any body load, which is applied whenever a PDE solve is required. Thus the precomputation cost is amortized over many PDE solves. This approach will make second order optimization algorithms computationally affordable for practical applications such as photoacoustic tomography and optimal design problems.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationGeldermans, Peter. "Accelerated PDE Constrained Optimization using Direct Solvers." (2018) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/105485">https://hdl.handle.net/1911/105485</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/105485en_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.subjectPDE constrained optimizationen_US
dc.subjectdirect solversen_US
dc.subjectfast solversen_US
dc.titleAccelerated PDE Constrained Optimization using Direct Solversen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputational and Applied Mathematicsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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