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Q:

What’s the optimal set of adjoint equations to solve for perturbed states?

In a nutshell, I’m working on a series of simple, sub-regional PDEs on Cartesian grids (very much like an engineering design problem). The simulation is approximated on the $N$-grid via a spatial finite difference method, and the PDEs are solved in time via a finite difference method. The discretized form of the PDEs in question is:
\begin{equation}
\frac{\partial\psi_{jk}}{\partial t} –
abla^2\phi_{jk} = s_j(x,t)
\end{equation}
where $\psi_{jk}$ is the state variable, $\phi_{jk}$ is the (adjoint) flux variable, and $s_j(x,t)$ is the random disturbance term (which is just a small perturbation added to the governing equation, to be multiplied by a factor of 10). My goal is to find the most optimal set of adjoint equations to solve for the flux variable given the set of state variables.
To help frame this question, I’d like to get a feel for what sort of solution space I’m working in. I’m assuming that for this problem that the solution is of the form $\psi_{jk} = \psi^\star_{jk} + s_j(x,t)$, where $\psi^\star_{jk}$ is the steady-state value of $\psi_{jk}$ for the given $\psi_{jk}$. I’m also guessing that this is a fairly linear problem (as it only involves a gradient, no non-linear terms).
In this case, the linearity of the problem allows me to do a basic analysis of the steady-state state of the problem (via the steady-state linearization of the problem), and I can solve for the steady-state states of the PDEs. My idea is that I’ll do the following for a given $\psi_{jk 384a16bd22

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– Create custom folders/directories, set a hotkey and assign a macro to them.
– It is recommended to create a folder with the name “”
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IP Address To Cursor Hotkey is a simple macro creation tool. It can be used to create keyboard macros and shortcuts.
It can be used with latest versions of Windows OS. It is compatible with “Alt” + Cursor key to change the cursor position. This macro can be set for a single keyboard shortcut or for multiple shortcuts to make this faster.
It can be used to rename any file or folder on the left hand side.
You can choose the position of the cursor on the active document window.
KeyMACRO
– Create custom folders/directories, set a hotkey and assign a macro to them.
– It is recommended to create a folder with the name “”
– You can select a directory by clicking on the folder.
– All icons are in ico format

IP Address To Cursor Hotkey is a simple macro creation tool. It can be used to create keyboard macros and shortcuts.
It can be used with latest versions of Windows OS. It is compatible with “Alt” + Cursor key to change the cursor position. This macro can be set for a single keyboard shortcut or for multiple shortcuts to make this faster.
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