Domain partitioning to bound moments of differential equations using semidefinite optimization
Name
85844111-MIT.pdf
Description
Full printable version
Size
2.9 MB
Format
Adobe PDF
Checksum (MD5)
af6b370051777191fa0a512f571f410d
Author(s)
Sethuraman, Sandeep
Advisor(s)
Pablo A. Parrilo.
Date Issued
2006
Publisher
Massachusetts Institute of Technology
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).
Subjects
Computation for Design and Optimization Program.
MIT Department
Massachusetts Institute of Technology. Computation for Design and Optimization Program
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