Optimal shape design in a fibre orientation model. (English) Zbl 1164.35353

Summary: 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.


35J55 Systems of elliptic equations, boundary value problems (MSC2000)
49Q10 Optimization of shapes other than minimal surfaces
49Q12 Sensitivity analysis for optimization problems on manifolds
76M10 Finite element methods applied to problems in fluid mechanics


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