| 1. |
- Johansson, Håkan, 1979, et al.
(author)
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Application-specific error control for parameter identification problems
- 2011
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In: International Journal for Numerical Methods in Biomedical Engineering. - : Wiley. - 2040-7939 .- 2040-7947. ; 27:4, s. 608-618
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Journal article (peer-reviewed)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.
(author)
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Calibration of a class of non-linear viscoelasticity models with adaptive error control
- 2007
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In: Computational Mechanics. - : Springer Science and Business Media LLC. - 1432-0924 .- 0178-7675. ; 41:1, s. 107-119
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Journal article (peer-reviewed)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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| 6. |
- Sandström, Carl, 1978, et al.
(author)
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A two-scale finite element formulation of Stokes flow in porous media
- 2013
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In: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825. ; 261, s. 96-104
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Journal article (peer-reviewed)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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| 7. |
- Sandström, Carl, 1978, et al.
(author)
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Multiscale modeling of porous media
- 2011
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In: Proceedings of NSCM-24, the 24th Nordic Seminar on Computational Mechanics. ; , s. 111-114
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Conference paper (peer-reviewed)
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| 8. |
- Sandström, Carl, 1978, et al.
(author)
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MULTISCALE MODELING OF POROUS MEDIA
- 2010
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In: Proceedings of NSCM-23, Anders Eriksson och Gunnar Tibert, Nordic Seminar on Computational Mechanics, Sockholm, 21-22 October 2010. - 0348-467X. ; 2010, s. 177-180
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Conference paper (peer-reviewed)abstract
- Homogenization of flow in porous media is studied. The continuity equation in conjunction with Darcy’s law as a constitutive relation on the macroscale, where the permeability is a function of the pressure gradient, is applied to a macroscopic domain. On the heterogenousmesoscale, a Stokes flow problem is formulated on a Representative Volume Element with a prescribed pressure gradient and suitable boundary condition. The numerical procedure for finite element simulations of the two-scale problem is outlined and illustrated by a few exampleproblems.
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