Reduced basis method for quantum models of crystalline solids

Electronic structure problems in solids usually involve repetitive determination of quantities of interest, evaluation of which requires the solution of an underlying partial differential equation. We present in this thesis the application of the reduced basis method in accurate and rapid evaluations of outputs associated with some nonlinear eigenvalue problems related to electronic structure calculations. The reduced basis method provides a systematic procedure by which efficient basis sets and computational strategies can be constructed. The essential ingredients are (i) rapidly convergent global reduced basis approximation spaces; (ii) an offline-online computational procedure to decouple the generation and projection stages of the approximation process; and (iii) inexpensive a posteriori error estimation procedure for outputs of interest. We first propose two strategies by which we can construct efficient reduced basis approximations for vectorial eigensolutions - solutions consisting of several eigenvectors. The first strategy exploits the optimality of the Galerkin procedure to find a solution in the span of all eigenvectors at N judiciously chosen samples in the parameter space.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mechanical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2007

Author dc:creator

• Pau, George Shu Heng

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/1721.1/40376

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/40376