Lancsoz solver for optimal transient growth

[loiseaujc]

Implement Lancsoz solver as a replacement for Arnoldi for transient growth computation. Need to simultaneously outpost the optimal initial perturbation and corresponding response.

[loiseaujc]

Not sure this feature is actually needed. Sure enough, some extra computation would be avoided (particularly in the orthogonalization step for the construction of the Hessenberg matrix) but since the bulk of computation is the matrix-vector product we wouldn't see much difference and it would only be a bit harder to maintain. What do you think ?

[ricardofrantz]

Agreed that the computation would not become significantly cheaper. The main benefit would be to find a way to compute both optimal initial condition and response on the same run. What options do we have?

[loiseaujc]

I was thinking to change a bit outpost_ks :

• If regular stability, outpost as it is at the moment
• If transient growth : run a forward linearized map initialized with the corresponding optimal perturbation and outpost both of them.

If we do so, we do not have to change anything in matvec nor in krylov_schur and we don't need to store two Krylov bases simultaneously.

[ricardofrantz]

😀

Em qua., 7 de abr. de 2021 às 09:57, Jean-Christophe < @.***> escreveu:

I was thinking to change a bit outpost_ks :

• If regular stability, outpost as it is at the moment
• If transient growth : run a forward linearized map initialized with the corresponding optimal perturbation and outpost both of them.

If we do so, we do not have to change anything in matvec nor in krylov_schur and we don't need to store two Krylov bases simultaneously.

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