  The shape dynamics of fluid vesicles is governed by the coupling of the flow
within the two-dimensional membrane to the hydrodynamics of the surrounding
bulk fluid. We present a numerical scheme which is capable of solving this flow
problem for arbitrarily shaped vesicles using the Oseen tensor formalism. For
the particular problem of simple shear flow, stationary shapes are found for a
large range of parameters. The dependence of the orientation of the vesicle and
the membrane velocity on shear rate and vesicle volume can be understood from a
simplified model.
