Domain partitioning to bound moments of differential equations using semidefinite optimization
Citable URI:
http://hdl.handle.net/1721.1/39213
| Title: | Domain partitioning to bound moments of differential equations using semidefinite optimization |
| Author: | Sethuraman, Sandeep |
| Other Contributors: | Massachusetts Institute of Technology. Computation for Design and Optimization Program. |
| Advisor: | Pablo A. Parrilo. |
| Department: | Massachusetts Institute of Technology. Computation for Design and Optimization Program. |
| Publisher: | Massachusetts Institute of Technology |
| Issue Date: | 2006 |
| Abstract: | 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. |
| Description: |
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006. Includes bibliographical references (leaf 95). |
| URI: | http://hdl.handle.net/1721.1/39213 |
| Keywords: | Computation for Design and Optimization Program. |
Files in this item
| Files | Size | Format |
|---|---|---|
| Preview, non-printable (open to all) | 3.038Mb | application/pdf |
| Full printable version (MIT only) | 3.038Mb | application/pdf |
This item appears in the following Collection(s)
All Items in DSpace@MIT are protected by original copyright, with all rights reserved, unless otherwise indicated.
|
|
Contact
MIT Libraries
|