Accelerated PDE Constrained Optimization using Direct Solvers

Simple item page
dc.contributor.advisorGillman, Adrianna
dc.contributor.committeeMemberHeinkenschloss, Matthias
dc.creatorGeldermans, Peter
dc.date.accessioned2019-05-16T20:12:09Z
dc.date.available2019-05-16T20:12:09Z
dc.date.created2018-05
dc.date.issued2018-04-17
dc.date.submittedMay 2018
dc.date.updated2019-05-16T20:12:09Z
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.
dc.format.mimetypeapplication/pdf
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>.
dc.identifier.urihttps://hdl.handle.net/1911/105485
dc.language.isoeng
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.
dc.subjectPDE constrained optimization
dc.subjectdirect solvers
dc.subjectfast solvers
dc.titleAccelerated PDE Constrained Optimization using Direct Solvers
dc.typeThesis
dc.type.materialText
thesis.degree.departmentComputational and Applied Mathematics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Arts
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
GELDERMANS-DOCUMENT-2018.pdf
Size:
15.28 MB
Format:
Adobe Portable Document Format
Download
License bundle
Now showing 1 - 2 of 2
No Thumbnail Available
Name:
PROQUEST_LICENSE.txt
Size:
5.85 KB
Format:
Plain Text
Description:
Download
No Thumbnail Available
Name:
LICENSE.txt
Size:
2.61 KB
Format:
Plain Text
Description:
Download
Collections
Rice University Electronic Theses and Dissertations