s]: [LAMBDA]: Diagonal matrix of eigenvalues [rho]: Fluid density [sigma]: Stress resultants [epsilon]: Vector containing membrane strains, curvatures, and shear strains [PSI]: Adjoint variable
vector [alpha]: Angle of attack [beta]: Angle of sideslip [bar.
where R is the real part operator and the adjoint variable
And we define the state and adjoint variable
S(t), I(t), T(t), R(t), [[lambda].
Then there exists a piecewise differentiable adjoint variable
The Adjoint variable
method (AVM) has been proposed for the acceleration of derivative-based optimization of microwave devices .
method for the thermal design of eutectic directional solidification processes in an open-boat configuration, -Numer.
i] may be calculated via the adjoint variable
method (see, e.
The computation of sensitivities is significantly streamlined by using the adjoint variable
Thus, to hold these adjoint values, it is sufficient to define one adjoint variable
for each variable.
This, on one hand, provides a closed-form expression for the optimal input as a function of the state and adjoint variables
, which will be used in solution methods based on shooting.
Thus, one can compute the adjoint variables
A(u) by solving the adjoint equation
2~(t) are the adjoint variables
for F(t) and I(t), respectively.