[WIP] Power Iteration Method for Numerical Stability Analysis of the Non-Linear System

[Bot-Enigma-0]

Proposed Changes

Give a brief overview of your contribution here in a few sentences.
We have a non-linear system described by x_{n+1} = F(x_n), where x_n and x_{n+1} are the solution states at time steps n and n+1, and F represents our nonlinear solver iteration. The spectral radius of the Jacobian matrix J_F = dF/dx determines the stability of our iterative scheme.

The power iteration method allows us to estimate the dominant eigenvalue (spectral radius) without explicitly forming the Jacobian matrix. The basic idea is:

1. Start with a random vector v
2. Repeatedly compute w = J_F * v (using forward-mode AD)
3. Normalize w to get the new v
4. The norm of w converges to the dominant eigenvalue of the system

The current version has some bugs leading to seg faults which i'm trying to debug. I would appreciate any comments.

Related Work

Resolve any issues (bug fix or feature request), note any related PRs, or mention interactions with the work of others, if any.

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[pcarruscag]

Appart from the nullptr issue with nodes. and missing mpi reduction, this looks correct 👍

[pcarruscag]

use su2matrix instead of vector passivedouble so you don't need to deal with the offset variable

[pcarruscag]

For multiple mpi ranks you need to reduce the norm and then take the square root and normalize the vector.

[pcarruscag]

nodes is nullptr in these calls. You don't need to pass nodes here, the solver owns its nodes.

The best way to fix the problem is to remove the declaration of the unused local variable targetSolver from the CFluidIteration::PreRunSpectralRadius function in SU2_CFD/src/iteration/CFluidIteration.cpp. No changes to functionality or imports are necessary as the variable is completely unused. The code can be safely deleted from line 781 with no other modifications required.

To fix the problem, remove the declaration unsigned short targetVar = 0; on line 782 in SU2_CFD/src/iteration/CFluidIteration.cpp. Since it's completely unused, removal improves readability and prevents any confusion. No other changes to code logic are needed, as no parts of the function refer to this variable.