Publication: Sensitivity of Optimal Shapes of Artificial Grafts with Respect to Flow Parameters
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Sensitivity of Optimal Shapes of Artificial Grafts with Respect to Flow Parameters

- Article in a journal -
 

Area
Computational Fluid Dynamics

Author(s)
M. Probst , M. Lülfesmann , M. Nicolai , H. M. Bücker , M. Behr , C. H. Bischof

Published in
Computer Methods in Applied Mechanics and Engineering

Year
2010

Abstract
The difficulties arising in the numerical solution of PDE-constrained shape optimization are manifold. An optimization algorithm iteratively generates updates for the design parameters, and mesh update techniques are required to automatically adjust the computational domain on which one or more solutions of the underlying PDE need to be computed. In blood-wetted medical devices, for example in artificial grafts, blood flow is described by the incompressible Navier-Stokes equations. Previous studies indicated the need for specific constitutive models to account for the non-Newtonian nature of blood that might affect the outcome when solving the shape optimization problem. In this paper, we propose a shape optimization framework that couples a highly-parallel finite element solver with a NURBS shape parametrization and BFGS-type optimizers. The entire optimization framework is transformed with automatic differentiation techniques, and the derivative code is employed to compute derivatives of the optimal shapes with respect to viscosity. This methodology provides a powerful tool to further investigate the necessity of intricate constitutive models by taking derivatives with respect to model parameters.

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ADIFOR, TAPENADE

BibTeX
@ARTICLE{
         Probst2010SoO,
       author = "M. Probst and M. L{\"u}lfesmann and M. Nicolai and H. M.
         B{\"u}cker and M. Behr and C. H. Bischof",
       title = "Sensitivity of Optimal Shapes of Artificial Grafts with Respect to Flow Parameters",
       journal = "Computer Methods in Applied Mechanics and Engineering",
       number = "17--20",
       pages = "997--1005",
       doi = "10.1016/j.cma.2009.11.013",
       abstract = "The difficulties arising in the numerical solution of PDE-constrained shape
         optimization are manifold. An optimization algorithm iteratively generates updates for the design
         parameters, and mesh update techniques are required to automatically adjust the computational domain
         on which one or more solutions of the underlying PDE need to be computed. In blood-wetted medical
         devices, for example in artificial grafts, blood flow is described by the incompressible
         Navier-Stokes equations. Previous studies indicated the need for specific constitutive models to
         account for the non-Newtonian nature of blood that might affect the outcome when solving the shape
         optimization problem. In this paper, we propose a shape optimization framework that couples a
         highly-parallel finite element solver with a NURBS shape parametrization and BFGS-type optimizers.
         The entire optimization framework is transformed with automatic differentiation techniques, and the
         derivative code is employed to compute derivatives of the optimal shapes with respect to viscosity.
         This methodology provides a powerful tool to further investigate the necessity of intricate
         constitutive models by taking derivatives with respect to model parameters.",
       year = "2010",
       volume = "199",
       ad_area = "Computational Fluid Dynamics",
       ad_tools = "ADIFOR, TAPENADE"
}


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