Reduced basis approximation and a posteriori error estimation for non-coercive elliptic problems : applications to acoustics

Modern engineering problems often require accurate, reliable, and efficient evaluation of quantities of interest, evaluation of which demands the solution of a partial differential equation. We present in this thesis a general methodology for the predicition of outputs of interest of non-coercive elliptic partial differential equations. The essential ingredients are: (i) rapidly convergent reduced basis approximations - Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter-time space; (ii) a posteriori error estimation - relaxations of the error-residual equation that provide rigorous and sharp bounds for the error in specific outputs of interest; and (iii) offline-online computational procedures - in the offline stage the reduced basis approximation is generated; in the online stage, given a new parameter value, we calculate the reduced basis output and associated error bound. The operation count for the online stage depends only on N (typically small) and the parametric complexity of the problem; the method is thus ideally suited for repeated, rapid, reliable evaluation of input-output relationships in the many-query or real-time contexts. We consider the crucial ingredients for the treatment of acoustics problems

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Civil and Environmental Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2007

Author dc:creator

• Sen, Sugata, 1977-

Advisor dc:contributor.advisor

• Anthony T. Patera.

• Civil and Environmental Engineering.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/39355

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/39355