Global ETD Search

1	Moment Matching and Modal Truncation for Linear Systems Hergenroeder, AJ 24 July 2013 (has links) 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. 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 system.