Sensitivity Analysis for Shallow Water Equations - Advanced Study ...
Sensitivity Analysis for Shallow Water Equations - Advanced Study ...
Sensitivity Analysis for Shallow Water Equations - Advanced Study ...
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Why an Adjoint Equation?<br />
Diffusion equation defined in the domain x ∈ (0, L) is<br />
Objective function :<br />
where r = δ(x − x T ).<br />
Adjoint Equation<br />
Objective function:<br />
where f = Mδ(x − x s ).<br />
D ∂2 C<br />
+ f = 0, C(0) = C(L) = 0<br />
∂x 2<br />
J =<br />
J =<br />
∫ L<br />
0<br />
r(x)C(x) dx<br />
D ∂2 C ∗<br />
∂x 2 + r = 0<br />
∫ L<br />
0<br />
f (x)C ∗ (x) dx<br />
Vani Cheruvu (ASP Research Review) Adjoint <strong>Sensitivity</strong> <strong>Analysis</strong> 06/14/2007 9 / 30
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