Reduced-basis methods applied to locally non-affine and locally non-linear partial differential equations

In modern engineering and scientific applications there is a huge demand for solutions of parameter-based partial differential equations and associated outputs of interest expressed as functionals of these solutions. Areas that require solving partial differential equations include - but are not restricted to heat transfer, elasticity, and fluid dynamics. Since in most cases it is not feasible to obtain an analytic solution, many numerical approaches to obtain approximate numerical solutions - such as finite elements. finite differences, finite volumes have been developed. For applications like optimization. design, and inverse problems, where it is crucial to evaluate the field solution/output repeatedly, it might be overly computationally expensive to apply conventional numerical methods. To address this issue we present and compare two new reduced basis techniques for the rapid and reliable prediction of linear functional outputs of linear elliptic partial differential equations with locally non-affine parameter dependence: the partition of unity method (PUM) and the minimax coefficient approximation method (MCAM). We also describe the minimax coefficient approximation method (MCAM) in application to locally non-linear elliptic partial differential equations.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mechanical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2005

Author dc:creator

• Solodukhov, Yuri Olegovich

Advisor dc:contributor.advisor

• Anthony T. Patera.

• Mechanical 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/1721.1/32390

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/32390