21.
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Parameter identification in constitutive models via optimization with a posteriori error control
Johansson, Håkan; Runesson, Kenneth
International journal for numerical methods in engineering,
14 March 2005, Letnik:
62, Številka:
10
Journal Article
Recenzirano
In this paper we outline a computational technique for the calibration of macroscopic constitutive laws with automatic error control. In the most general situation the state variables of the ...
constitutive law, as well as the material parameters, are spatially non‐homogeneous. The experimental observations are given in space–time. Based on an appropriate dual problem, we compute a posteriori the discretization error contributions from approximations of the parameter, state and costate fields in space–time for an arbitrarily chosen goal‐oriented error measure of engineering significance. Such a measure can be used in an adaptive strategy (not discussed in this paper) to meet a predefined error tolerance. An important observation is that the Jacobian matrix associated with the resulting Newton method is used (in principle) in solving the dual problem. Rather than treating the Jacobian in a monolithic fashion, we utilize a sequential solution strategy, whereby the FE‐topology of the discretized state problem is used repeatedly. Moreover, the proposed solution strategy lends itself naturally to the computation of first and second order sensitivities, which are obtained with little extra computational effort. Numerical results are given for the prototype model of confined aquifer flow with spatially non‐homogeneous permeability. The efficiency of the optimization strategy and the effectivity of the error computation are assessed. Copyright © 2005 John Wiley & Sons, Ltd.
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Celotno besedilo
Dostopno za:
BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
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22.
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A posteriori error estimation of approximate boundary fluxes
Wildey, T.; Tavener, S.; Estep, D.
Communications in numerical methods in engineering,
June 2008, Letnik:
24, Številka:
6
Journal Article, Conference Proceeding
This paper describes the a posteriori estimation of the error in the flux of a finite element approximation on a piece of the boundary of the domain. The estimate is obtained via a generalized ...
Green's function corresponding to the quantity of interest on the boundary. We investigate the effects of smoothing the data corresponding to the quantity of interest and explore the effective domain of dependence of the quantity. We relate this approach to previous work by M. F. Wheeler, G. F. Carey, I. Babuska et al., and M. Larson et al. Copyright © 2007 John Wiley & Sons, Ltd.
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Celotno besedilo
Dostopno za:
BFBNIB, FZAB, GIS, IJS, IZUM, KILJ, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBMB, UL, UM, UPUK
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