Discrete variational adjoint assimilations for parameter optimizations via spectral methods

Figures & data

Table 1. Comparison on the storage and computational cost for G1 and G2.

Algorithm	Storage	Cost
G1		O(N^3M)
G2	–	O(N^2M)

Table 2. Comparison on the storage and computational cost for L1 and L2.

Algorithm	Storage	Cost
L1		O(N^3)
L2	–	O(N^2M)

Figure 1. Convergence history of the objective function (a) and (e⁰)⁽ⁱ⁾ (b) in the complete assimilation.

Figure 2. Convergence history of the objective function (a) and (e⁰)⁽ⁱ⁾ (b) in the incomplete assimilation.

Figure 3. Same as in Figure 1 except for the initial guess.

Figure 4. Same as in Figure 2 except for the initial guess.

Figure 5. The convergence rate of the objective function and error of initial condition at the optimal state in the complete case (a) and incomplete case (b).

Figure 6. Comparison of different methods for determination of the step size (a) convergence history of the objective function (b) obtained step sizes.

Figure 7. Impact of γ on the convergence property of the minimization algorithm.