• Volume: 52, Issue: 5, page 391-405
• ISSN: 0862-7940

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## Abstract

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We study a 2D model of the orientation distribution of fibres in a paper machine headbox. The goal is to control the orientation of fibres at the outlet by shape variations. The mathematical formulation leads to an optimization problem with control in coefficients of a linear convection-diffusion equation as the state problem. Existence of solutions both to the state and the optimization problem is analyzed and sensitivity analysis is performed. Further, discretization is done and a numerical example is shown.

## How to cite

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Stebel, Jan, Mäkinen, Raino, and Toivanen, Jukka I.. "Optimal shape design in a fibre orientation model." Applications of Mathematics 52.5 (2007): 391-405. <http://eudml.org/doc/33297>.

@article{Stebel2007,
abstract = {We study a 2D model of the orientation distribution of fibres in a paper machine headbox. The goal is to control the orientation of fibres at the outlet by shape variations. The mathematical formulation leads to an optimization problem with control in coefficients of a linear convection-diffusion equation as the state problem. Existence of solutions both to the state and the optimization problem is analyzed and sensitivity analysis is performed. Further, discretization is done and a numerical example is shown.},
author = {Stebel, Jan, Mäkinen, Raino, Toivanen, Jukka I.},
journal = {Applications of Mathematics},
keywords = {fibre suspension flow; convection-diffusion equation; optimal control; sensitivity analysis; finite element method; automatic differentiation; fibre suspension flow; convection-diffusion equation; optimal control; sensitivity analysis},
language = {eng},
number = {5},
pages = {391-405},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
url = {http://eudml.org/doc/33297},
volume = {52},
year = {2007},
}

TY - JOUR
AU - Stebel, Jan
AU - Mäkinen, Raino
AU - Toivanen, Jukka I.
JO - Applications of Mathematics
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 5
SP - 391
EP - 405
AB - We study a 2D model of the orientation distribution of fibres in a paper machine headbox. The goal is to control the orientation of fibres at the outlet by shape variations. The mathematical formulation leads to an optimization problem with control in coefficients of a linear convection-diffusion equation as the state problem. Existence of solutions both to the state and the optimization problem is analyzed and sensitivity analysis is performed. Further, discretization is done and a numerical example is shown.
LA - eng
KW - fibre suspension flow; convection-diffusion equation; optimal control; sensitivity analysis; finite element method; automatic differentiation; fibre suspension flow; convection-diffusion equation; optimal control; sensitivity analysis
UR - http://eudml.org/doc/33297
ER -

## References

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8. Shape optimization in problems governed by generalised Navier-Stokes Equations: Existence analysis, Control Cybern. 34 (2005), 283–303. (2005) MR2211072
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11. 10.1002/cnm.833, Commun. Numer. Meth. Eng.; Published Online: 13  Dec  2005, DOI: 10.1002/cnm.833. MR2235029DOI10.1002/cnm.833
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