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Though fluid dynamics offer a good approach to nonrigid registration and give accurate results, even with large-scale deformations, its application is still very time consuming. We introduce and discuss different approaches to solve the core problem of nonrigid registration, the partial differential equation of fluid dynamics. We focus on the solvers, their computational costs and the accuracy of registration. Numerical experiments show that relaxation is currently the best approach, especially when reducing the cost/iteration by focusing the updates on deformation spots.