[Zhen ZHANG]

Hi all,
I recently studied the discrete adjoint solver because I want to add some space varying design variables. I also learned the CoDi package. Here are my
understanding and questions.
Assuming f is the objective function, g is the control equation, p is the design variable, and x is the flow variable.
In an adjoint problem, we want to get df/dp. Let f_p be the partial derivative (f_p=partial f/partial p). We get

df/dp=f_p+lambda^T*g_p

where lambda is the adjoint variable and satisfies

(g_x)^T*lambda=-(f_x)^T

But in the solver, after starting recording, we register the solution and variables as the input, set dependencies, direct run, register the solution and the objective function as the output, and stop recording.

Q1: why do we need to register the solution of the direct solver as the output? Now they are both input and output.

And then in CDiscAdjSinglezoneDriver::Run(), we initialize the adjoint of the direct solver using the adjoint solver solution of the last step, set the derivative of the objective function as 1.0, compute the adjoint, extract derivatives of the solution and variables.

Q2: What are the derivatives of the solution and variables here? In the reverse mode and with the obj func derivative set to 1.0, they should be partial f/partial(). Is that right?

Q3: What does this iteration do? How does it solve the above adjoint equation?

Maybe there are some mistakes in the statement due to my limited understanding. I am grateful if you point them out.
Thank you!