Geodesic
Optimal shape design in a fibre orientation model
Applications of Mathematics, Tome 52 (2007) no. 5, pp. 391-405

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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.
DOI : 10.1007/s10492-007-0022-5
Classification : 35J55, 49Q10, 49Q12, 76M10
Keywords: fibre suspension flow; convection-diffusion equation; optimal control; sensitivity analysis; finite element method; automatic differentiation 
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Stebel, Jan; Mäkinen, Raino A. E.; Toivanen, Jukka I. Optimal shape design in a fibre orientation model. Applications of Mathematics, Tome 52 (2007) no. 5, pp. 391-405. doi: 10.1007/s10492-007-0022-5

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