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Low‐dimensional I/O modeling of Distributed Parameter Systems
Author(s) -
Schmidt Michael
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610005
Subject(s) - discretization , lti system theory , discretization error , reduction (mathematics) , mathematics , invariant (physics) , representation (politics) , operator (biology) , matrix (chemical analysis) , linear system , computer science , mathematical optimization , mathematical analysis , geometry , biochemistry , chemistry , materials science , repressor , mathematical physics , gene , composite material , politics , political science , law , transcription factor
Abstract Many model reduction techniques take a semi‐discretization of the original PDE model as starting point and aim then at an accurate approximation of its input/output map. In this contribution, we discuss the direct discretization of the i/o map of the original infinite‐dimensional system. First, the input and output signals are discretized in space and time, second, the system dynamics are approximated in form of the underlying evolution operator, leading to an approximated i/o map with matrix representation. The discretization framework, corresponding error estimations, a SVD‐based system reduction method and a numerical application in an optimization problem are presented for the example of a linear time‐invariant heat equation. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)