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- Johansson, Håkan, 1979, et al.
(författare)
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Application-specific error control for parameter identification problems
- 2011
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Ingår i: International Journal for Numerical Methods in Biomedical Engineering. - : Wiley. - 2040-7939 .- 2040-7947. ; 27:4, s. 608-618
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Tidskriftsartikel (refereegranskat)abstract
- An often occurring scenario in the mathematical modeling of physical phenomena is that of a two-step computation consisting of, first, identifying a relevant parameter set from experiments (such as material parameters) and, second, carrying out a subsequent simulation using these parameters. In order to ensure the quality of the results from the simulation, the different sources of errors, for example, from discretization and inexact solution, must be traced and properly reduced. In this paper, a previously developed method for goal-oriented a posteriori error estimation for identification problems is extended to accommodate the combined identification and subsequent simulation. © 2009 John Wiley & Sons, Ltd.
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| 2. |
- Johansson, Håkan, 1979, et al.
(författare)
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Calibration of a class of non-linear viscoelasticity models with adaptive error control
- 2007
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Ingår i: Computational Mechanics. - : Springer Science and Business Media LLC. - 1432-0924 .- 0178-7675. ; 41:1, s. 107-119
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Tidskriftsartikel (refereegranskat)abstract
- The calibration of constitutive models is considered as an optimization problem where parameter values are sought to minimize the discrepancy between measured and simulated response. Since a finite element method is used to solve an underlying state equation, discretization errors arise, which induce errors in the calibrated parameter values. In this paper, adaptive mesh refinement based on the pertinent dual solution is used in order to reduce discretization errors in the calibrated material parameters. By a sensitivity assessment, the influence from uncertainties in experimental data is estimated, which serves as a threshold under which there is no need to further reduce the discretization error. The adaptive strategy is employed to calibrate a viscoelasticity model with observed data from uniaxial compression (i.e., homogeneous stress state), where the FE-discretization in time is studied. The a posteriori error estimations show an acceptable quality in terms of effectivity measures. © 2007 Springer Verlag.
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| 3. |
- Johansson, Håkan, 1979, et al.
(författare)
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Calibration of a class of non-linear viscoelasticity models with sensitivity assessment based on duality
- 2007
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 69:12, s. 2513-2537
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Tidskriftsartikel (refereegranskat)abstract
- The calibration of constitutive models is based on the solution of an optimization problem, whereby the sought parameter values minimize an objective function that measures the discrepancy between experimental observations and the corresponding simulated response. By the introduction of an appropriate adjoint problem, the resulting formulation becomes well suited for a gradient-based optimization scheme. A class of viscoelastic models is studied, where a discontinuous Galerkin method is used to integrate the governing evolution equation in time. A practical solution algorithm, which utilizes the time-flow structure of the underlying evolution equation, is presented. Based on the proposed formulation it is convenient to estimate the sensitivity of the calibrated parameters with respect to measurement noise. The sensitivity is computed using a dual method, which compares favourably with the conventional primal method. The strategy is applied to a viscoelasticity model using experimental data from a uniaxial compression test. Copyright © 2006 John Wiley & Sons, Ltd.
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| 4. |
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| 5. |
- Johansson, Håkan, 1979, et al.
(författare)
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Calibration of a nonlinear viscoelasticity model with sensitivity assessment
- 2005
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Ingår i: Constitutive Models for Rubber IV, edited by P.-E. Austrell & L. Kari. - 0415383463 ; , s. 341-347
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Konferensbidrag (refereegranskat)abstract
- The calibration of constitutive models isbased on the solution of an optimization problem, where parameter values are sought such that optimal correspondence between measured and simulated response is achieved. The calibration problem is solved using a recently proposed strategy, which has the advantage that discretization errors induced in the simulated response, leading to errors in the optimal parameter values, isrelatively straightforward to estimate. Furthermore, it ispossible to estimate how sensitive the obtained solution is to uncertainties in the experimental data.
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| 6. |
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| 7. |
- Johansson, Håkan, 1979, et al.
(författare)
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Parameter identification in constitutive models via optimization with a posteriori error control
- 2005
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Ingår i: International Journal for Numerical Methods in Engineering. ; 62:10, s. 1315-1340
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we outline a computational technique for the calibration of macroscopic constitutive lawswith 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 aregiven in spacetime. Based on an appropriate dual problem, we compute a posteriori the discretizationerror contributions from approximations of the parameter, state and costate fields in spacetime foran arbitrarily chosen goal-oriented error measure of engineering significance. Such a measure can beused in an adaptive strategy (not discussed in this paper) to meet a predefined error tolerance. Animportant 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 isused repeatedly. Moreover, the proposed solution strategy lends itself naturally to the computation offirst and second order sensitivities, which are obtained with little extra computational effort. Numericalresults are given for the prototype model of confined aquifer flow with spatially non-homogeneouspermeability. The efficiency of the optimization strategy and the effectivity of the error computationare assessed.
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| 9. |
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| 10. |
- Sandström, Carl, 1978, et al.
(författare)
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A two-scale finite element formulation of Stokes flow in porous media
- 2013
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825. ; 261, s. 96-104
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Tidskriftsartikel (refereegranskat)abstract
- Seepage through saturated porous material with an open pore system is modeled as a non-linear Stokes flow through a rigid matrix. Based on variationally consistent homogenization, the resulting macroscale problem becomes a Darcy-type flow. The prolongation of the Darcy flow fulfills a macrohomogeneity condition, which in a Galerkin context implies a symmetric macroscale problem. The homogenization is of 1st order and periodic boundary conditions are adopted on a Representative Volume Element. A nonlinear nested multiscale technique, in which the subscale problem is used as a constitutive model, is devised. In the presented numerical investigation, the effects of varying physical parameters as well as of the discretization are considered. In particular, it is shown that the two-scale results agree well with those of the fully resolved fine-scale problem.
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