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Embree, Mark Sorensen, Danny C. Warburton, Tim Hergenroeder, AJ 2013-07-24T19:31:24Z 2013-07-24T19:31:27Z 2013-07-24T19:31:24Z 2013-07-24T19:31:27Z 2012-12 2013-07-24 December 2012 2013-07-24T19:31:27Z Hergenroeder, AJ. "Moment Matching and Modal Truncation for Linear Systems." (2013) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/71657">https://hdl.handle.net/1911/71657</a>. https://hdl.handle.net/1911/71657 123456789/ETD-2012-12-328 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. application/pdf eng 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. 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 Moment Matching and Modal Truncation for Linear Systems Thesis Text Computational and Applied Mathematics Engineering Rice University Masters Master of Arts open.access