Inverse problem of shape identification from boundary measurement for Stokes equations: Shape differentiability of Lagrangian
Keyword(s):
AbstractFor Stokes equations under divergence-free and mixed boundary conditions, the inverse problem of shape identification from boundary measurement is investigated. Taking the least-square misfit as an objective function, the state-constrained optimization is treated by using an adjoint state within the Lagrange approach. The directional differentiability of a Lagrangian function with respect to shape variations is proved within the velocity method, and a Hadamard representation of the shape derivative by boundary integrals is derived explicitly. The application to gradient descent methods of iterative optimization is discussed.
2009 ◽
Vol 43
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pp. 1185-1201
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2016 ◽
Vol 24
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pp. 449-457
2002 ◽
Vol 129
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pp. 237-267
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2015 ◽
Vol 53
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pp. 3006-3039
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2004 ◽
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pp. 807-826
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2001 ◽
Vol 21
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pp. 171-181
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