A monolithic one-velocity-field optimal control formulation for fluid-structure interaction problems with large solid deformation

In this article, we formulate a monolithic optimal control method for general time-dependent Fluid-Structure Interaction (FSI) systems with large solid deformation. We consider a displacement-tracking type of objective with a constraint of the solid velocity, tackle the time-dependent control problems by a piecewise-in-time control, cope with large solid displacement using a one-velocity fictitious domain method, and solve the fully-coupled FSI and the corresponding adjoint equations in a monolithic manner. We implement the proposed method in the open-source software package FreeFEM++ and assess it by three numerical experiments, in the aspects of stability of the numerical scheme for different regularisation parameters, and efficiency of reducing the objective function with control of the solid velocity.