Shape Hessian for generalized Oseen flow by differentiability of a minimax: A Lagrangian approach

Zhiming Gao; Yichen Ma; Hong Wei Zhuang

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 3, page 987-1011
  • ISSN: 0011-4642

Abstract

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The goal of this paper is to compute the shape Hessian for a generalized Oseen problem with nonhomogeneous Dirichlet boundary condition by the velocity method. The incompressibility will be treated by penalty approach. The structure of the shape gradient and shape Hessian with respect to the shape of the variable domain for a given cost functional are established by an application of the Lagrangian method with function space embedding technique.

How to cite

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Gao, Zhiming, Ma, Yichen, and Zhuang, Hong Wei. "Shape Hessian for generalized Oseen flow by differentiability of a minimax: A Lagrangian approach." Czechoslovak Mathematical Journal 57.3 (2007): 987-1011. <http://eudml.org/doc/31177>.

@article{Gao2007,
abstract = {The goal of this paper is to compute the shape Hessian for a generalized Oseen problem with nonhomogeneous Dirichlet boundary condition by the velocity method. The incompressibility will be treated by penalty approach. The structure of the shape gradient and shape Hessian with respect to the shape of the variable domain for a given cost functional are established by an application of the Lagrangian method with function space embedding technique.},
author = {Gao, Zhiming, Ma, Yichen, Zhuang, Hong Wei},
journal = {Czechoslovak Mathematical Journal},
keywords = {shape sensitivity analysis; shape Hessian; Eulerian semiderivative; differentiability of a minimax; Oseen flow; shape sensitivity analysis; shape Hessian; Eulerian semiderivative; differentiability of a minimax; Oseen flow},
language = {eng},
number = {3},
pages = {987-1011},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Shape Hessian for generalized Oseen flow by differentiability of a minimax: A Lagrangian approach},
url = {http://eudml.org/doc/31177},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Gao, Zhiming
AU - Ma, Yichen
AU - Zhuang, Hong Wei
TI - Shape Hessian for generalized Oseen flow by differentiability of a minimax: A Lagrangian approach
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 3
SP - 987
EP - 1011
AB - The goal of this paper is to compute the shape Hessian for a generalized Oseen problem with nonhomogeneous Dirichlet boundary condition by the velocity method. The incompressibility will be treated by penalty approach. The structure of the shape gradient and shape Hessian with respect to the shape of the variable domain for a given cost functional are established by an application of the Lagrangian method with function space embedding technique.
LA - eng
KW - shape sensitivity analysis; shape Hessian; Eulerian semiderivative; differentiability of a minimax; Oseen flow; shape sensitivity analysis; shape Hessian; Eulerian semiderivative; differentiability of a minimax; Oseen flow
UR - http://eudml.org/doc/31177
ER -

References

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