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- W2028699093 abstract "Abstract We consider parameter-dependent time-periodic parabolic problems as they occur e.g. in the modeling of rotating propellers. The goal is to determine the parameters (e.g. design or steering parameters) such that a given output of interest (e.g. the efficiency of the propeller) is maximized. A standard approach to numerically solve such problems is a time-stepping (fixed-point) scheme. This approach, however, often suffers from some drawbacks, in particular within the Reduced Basis Method (RBM). First, there might be long transient phases before a periodic or steady state is reached, which is particularly disadvantageous in the online phase. Moreover, corresponding error estimates usually include sums over time-steps which might become inaccurate. Instead, we consider a space-time variational formulation using periodic basis functions in time, which avoids the need for fixed-point iterations. Based on this variational formulation, we develop a space-time RBM using wavelets in time and derive corresponding a-posteriori error estimates. We present numerical results indicating the efficiency of the method as well as the effectivity of the derived error bounds." @default.
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- W2028699093 date "2012-01-01" @default.
- W2028699093 modified "2023-09-26" @default.
- W2028699093 title "Space-Time Reduced Basis Methods for Time-Periodic Partial Differential Equations" @default.
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- W2028699093 doi "https://doi.org/10.3182/20120215-3-at-3016.00126" @default.
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