Clarification Required on the solve_linear Method in DAFoamSolver within DAFOAM Source Code

[lnhang0618]

Hello Professor He Ping,

I hope this message finds you well. I have been reviewing the DAFOAM source code and have come across a snippet in the solve_linear method within DAFoamSolver that has left me puzzled.

Here is the portion of the code I am referring to:

# right hand side array from d_outputs
dFdWArray = d_outputs["%s_states" % self.discipline]

I am struggling to comprehend the exact functioning of this part. Based on my understanding of the apply_linear definition, it seems that d_output["aero_states"] should be equivalent to dRdw ^T * d_residual, implying that it represents dw in rev mode . This leads me to question why, in this scenario, dFdW is equated to dw. Is this a correct interpretation, or am I missing something in my understanding?

[lnhang0618]

But the function looks like a process in paper.

[friedenhe]

Your understanding of how the apply_linear function works is correct. This function computes the matrix-vector products for dRdInput^T*d_residual["states"]. However, for the solver_linear function, the d_ouputs dict saves the dFdW vector instead of the seed for matrix-vector products. The solve_linear solves the adjoint equation and output the adjoint vector psi, instead of matrix-vector products. So, apply_linear and solve_linear have very different input/output structures. solver_linear corresponds to the block 5 and apply_linear corresponds to the block 7 in the above diagram.