Moment Matching and Modal Truncation for Linear Systems

While moment matching can effectively reduce the dimension of a linear, time-invariant system, it can simultaneously fail to improve the stable time-step for the forward Euler scheme. In the context of a semi-discrete heat equation with spatially smooth forcing, the high frequency modes are virtually insignificant. Eliminating such modes dramatically improves the stable time-step without sacrificing output accuracy. This is accomplished by modal filtration, whose computational cost is relatively palatable when applied following an initial reduction stage by moment matching. A bound on the norm of the difference between the transfer functions of the moment-matched system and its modally-filtered counterpart yields an intelligent choice for the mode of truncation. The dual-stage algorithm disappoints in the context of highly nonnormal semi-discrete convection-diffusion equations. There, moment matching can be ineffective in dimension reduction, precluding a cost-effective modal filtering step.

Name thesis:degree_name

Master of Arts

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Engineering

Grantor

Rice University

Year dc:date.issued

2013

Author dc:creator

• Hergenroeder, AJ

Advisor dc:contributor.advisor

• Embree, Mark

Committee members dc:contributor.committeemember

• Sorensen, Danny C.
• Warburton, Tim

• Modal truncation
• Model reduction
• Moment matching
• Dual-stage dimension reduction
• Lanczos
• Arnoldi
• Smoothness
• Discrete smoothness
• Laplacian
• Heat equation
• Convection-diffusion
• Initial boundary value problem
• Fourier series
• Coefficient decay
• Semi-discrete
• Explicit integration
• Forward Euler
• Linear time-invariant systems

Statement dc:rights

• Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1911/71657

OAI identifier oai:identifier

oai:repository.rice.edu:1911/71657