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.
| Identifer | oai:union.ndltd.org:RICE/oai:scholarship.rice.edu:1911/71657 |
| Date | 24 July 2013 |
| Creators | Hergenroeder, AJ |
| Contributors | Embree, Mark |
| Source Sets | Rice University |
| Language | English |
| Detected Language | English |
| Type | thesis, text |
| Format | application/pdf |
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