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**Harvard**

Johansson, H. och Runesson, K. (2005) *Parameter identification in constitutive models via optimization with a posteriori error control *.

** BibTeX **

@article{

Johansson2005,

author={Johansson, Håkan and Runesson, Kenneth},

title={Parameter identification in constitutive models via optimization with a posteriori error control },

journal={International Journal for Numerical Methods in Engineering},

volume={62},

issue={10},

pages={1315-1340},

abstract={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 spacetime. Based on an appropriate dual problem, we compute a posteriori the discretization
error contributions from approximations of the parameter, state and costate ﬁelds in spacetime 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.},

year={2005},

keywords={parameter identiﬁcation, goal-oriented error estimate, sensitivity analysis},

}

** RefWorks **

RT Journal Article

SR Print

ID 3422

A1 Johansson, Håkan

A1 Runesson, Kenneth

T1 Parameter identification in constitutive models via optimization with a posteriori error control

YR 2005

JF International Journal for Numerical Methods in Engineering

VO 62

IS 10

SP 1315

OP 1340

AB 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 spacetime. Based on an appropriate dual problem, we compute a posteriori the discretization
error contributions from approximations of the parameter, state and costate ﬁelds in spacetime 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.

LA eng

OL 30