Domain partitioning to bound moments of differential equations using semidefinite optimization
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2007
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| Online Access: | http://hdl.handle.net/1721.1/39213 |
| _version_ | 1826201408452427776 |
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| author | Sethuraman, Sandeep |
| author2 | Pablo A. Parrilo. |
| author_facet | Pablo A. Parrilo. Sethuraman, Sandeep |
| author_sort | Sethuraman, Sandeep |
| collection | MIT |
| description | Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006. |
| first_indexed | 2024-09-23T11:51:09Z |
| format | Thesis |
| id | mit-1721.1/39213 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T11:51:09Z |
| publishDate | 2007 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/392132019-04-12T14:39:51Z Domain partitioning to bound moments of differential equations using semidefinite optimization Sethuraman, Sandeep Pablo A. Parrilo. Massachusetts Institute of Technology. Computation for Design and Optimization Program. Massachusetts Institute of Technology. Computation for Design and Optimization Program. Computation for Design and Optimization Program. Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006. Includes bibliographical references (leaf 95). In this thesis, we present a modification of an existing methodology to obtain a hierarchy of lower and upper bounds on moments of solutions of linear differential equations. The motivation for change is to obtain tighter bounds by solving smaller semidefinite problems. The modification we propose involves partitioning the domain and normalizing each partition to ensure numerical stability. Using the adjoint operator, linear constraints involving the boundary conditions and moments of the solution are developed for each partition. Semidefinite constraints are imposed on the moments, and an optimization problem is solved to obtain the bounds. We have demonstrated the algorithm by calculating bounds on moments of various one-dimensional case differential equations including the Bessel ODE, and Legendre polynomials. In the two-dimensional case we have demonstrated the algorithm by calculating bounds on various PDEs including the Helmholtz equation, and heat equation. In both cases, the results were encouraging with tighter bounds on moments being obtained by solving smaller problems with domain partitioning. by Sandeep Sethuraman. S.M. 2007-10-19T20:31:58Z 2007-10-19T20:31:58Z 2006 2006 Thesis http://hdl.handle.net/1721.1/39213 85844111 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 95 leaves application/pdf Massachusetts Institute of Technology |
| spellingShingle | Computation for Design and Optimization Program. Sethuraman, Sandeep Domain partitioning to bound moments of differential equations using semidefinite optimization |
| title | Domain partitioning to bound moments of differential equations using semidefinite optimization |
| title_full | Domain partitioning to bound moments of differential equations using semidefinite optimization |
| title_fullStr | Domain partitioning to bound moments of differential equations using semidefinite optimization |
| title_full_unstemmed | Domain partitioning to bound moments of differential equations using semidefinite optimization |
| title_short | Domain partitioning to bound moments of differential equations using semidefinite optimization |
| title_sort | domain partitioning to bound moments of differential equations using semidefinite optimization |
| topic | Computation for Design and Optimization Program. |
| url | http://hdl.handle.net/1721.1/39213 |
| work_keys_str_mv | AT sethuramansandeep domainpartitioningtoboundmomentsofdifferentialequationsusingsemidefiniteoptimization |