Sensitivity and Approximation of Coupled Fluid-Structure Equations by Virtual Control Method |
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Authors: | Cornel Marius Murea Carlos Vázquez |
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Institution: | (1) Laboratoire de Mathematiques, Universite de Haute-Alsace, 4 rue des Freres Lumiere, 68093 Mulhouse, France;(2) Departamento de Matematicas, Facultad de Informatica, Universidade da Coruna, Campus Elvina s/n, 15071 La Coruna, Spain |
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Abstract: | 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. |
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Keywords: | Fluid--structure interaction Virtual control Mixed formulations Optimization algorithms Sensitivity analysis |
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