# Optimal shape design in a fibre orientation model

Jan Stebel; Raino Mäkinen; Jukka I. Toivanen

Applications of Mathematics (2007)

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

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topStebel, 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},

title = {Optimal shape design in a fibre orientation model},

url = {http://eudml.org/doc/33297},

volume = {52},

year = {2007},

}

TY - JOUR

AU - Stebel, Jan

AU - Mäkinen, Raino

AU - Toivanen, Jukka I.

TI - Optimal shape design in a fibre orientation model

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 -

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