Frei, S.S.FreiAndrä, H.H.AndräPinnau, R.R.PinnauTse, O.O.Tse2022-03-042022-03-042015https://publica.fraunhofer.de/handle/publica/23906010.1007/s10589-013-9630-zWe present an efficient algorithm to find an optimal fiber orientation in composite materials. Within a two-scale setting fiber orientation is regarded as a function in space on the macrolevel. The optimization problem is formulated within a function space setting which makes the imposition of smoothness requirements straightforward and allows for rather general convex objective functionals. We show the existence of a global optimum in the Sobolev space H1(). The algorithm we use is a one level optimization algorithm which optimizes with respect to the fiber orientation directly. The costly solve of a big number of microlevel problems is avoided using coordinate transformation formulas. We use an adjoint-based gradient type algorithm, but generalizations to higher-order schemes are straightforward. The algorithm is tested for a prototypical numerical example and its behaviour with respect to mesh independence and dependence on the regularization parameter is studied.en519journal article