Applied Mathematics and Optimization

, Volume 52, Issue 2, pp 183–218 | Cite as

Sensitivity and Approximation of Coupled Fluid-Structure Equations by Virtual Control Method

  • Cornel Marius MureaEmail author
  • Carlos VázquezEmail author


The formulation of a particular fluid--structure interaction as an optimal control problem is the departure point of this work. The control is the vertical component of the force acting on the interface and the observation is the vertical component of the velocity of the fluid on the interface. This approach permits us to solve the coupled fluid--structure problem by partitioned procedures. The analytic expression for the gradient of the cost function is obtained in order to devise accurate numerical methods for the minimization problem. Numerical results arising from blood flow in arteries are presented. To solve the optimal control problem numerically, we use a quasi-Newton method which employs the analytic gradient of the cost function and the approximation of the inverse Hessian is updated by the Broyden, Fletcher, Goldforb, Shano (BFGS) scheme. This algorithm is faster than fixed point with relaxation or block Newton methods.

Fluid--structure interaction Virtual control Mixed formulations Optimization algorithms Sensitivity analysis 


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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Laboratoire de Mathematiques, Universite de Haute-Alsace, 4 rue des Freres Lumiere, 68093 MulhouseFrance

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