Reduced basis method for 2nd order wave equation : application to one-dimensional seismic problem

In this thesis, we solve the 2nd order wave equation, which is hyperbolic and linear in nature, to determine the pressure distribution for a one-dimensional seismic problem with smooth initial pressure and rate of pressure change with time. With Dirichlet and Neumann boundary conditions, the pressure distribution is solved for a total of 500 time steps, which is slighter more than a periodic cycle. Our focus is on the dependence of the output, the average surface pressure as it varies with time, on the system parameters ,u, which consist of the earthquake source x8 and the occurring time T. The reduced basis method, the offline-online computational procedures and the associated a posteriori error estimation are developed. We have shown that the reduced basis pressure distribution is an accurate approximation to the finite element pressure distribution. The greedy algorithm, the procedure of selecting the basis vectors which span the reduced basis space, works reasonably well although a period of slow convergence is experienced: this is because the finite element pressure distribution along the edges of the earthquake source-time space are fairly "unique" and cannot be accurately represented as a linear combination of the existing basis vectors;

Department dc:contributor.department

Massachusetts Institute of Technology. Computation for Design and Optimization Program.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Tan Yong Kwang, Alex

Advisor dc:contributor.advisor

• Anthony T. Patera.

• Computation for Design and Optimization Program.

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/1721.1/39209

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/39209