Doubt with EVP problem

[Miriam Rodríguez Sánchez]

Hello,

I am trying  to solve this equation ( Linear Adiabatic Wave Equation, attached)

in two different ways:

- the first one as a EVP 

- the second one I fix a eigenvalue I know from another program and I do LBVP.

I am obtaining some strange things and I want to verify if I am using correctly the tau operators or / and I have to use the lift operators or it is something related to the data.

I would appreciate the help,

thanks

Miriam RS

[Geoffrey Vasil]

Hi Miriam, 

- the first one as a EVP 

Hopefully this works. It should in principle if everything’s in setup correctly. 

- the second one I fix a eigenvalue I know from another program and I do LBVP.

This is unlikely to work in many situations (but I might sometimes). The reason is that linear equations are by definition badly behaved at eigenvalues, ( e.g. ( A-z*I ) x = 0, if z is an eigenvalue ). In principle, it’s possible to find null spaces (i.e. solutions to ( A-z*I ).x = 0), but dedalus isn’t easily setup to do this. It’s possible, but by-far the best thing to do is use an EVP, which is exactly what this is for. 

If you want to use a previous eigenvalue from another code as a guess you can do this easily with dedalus. Suppose you’re trying to solve A.x = z * x. And you think z ~ z0. You can define ( A-z0*I )x = z1 * x and treat z1 as the eigenvalue. If your guess is good then z1 should come out very small. 

Does this make sense? 

Cheers,

Geoff 

I am obtaining some strange things and I want to verify if I am using correctly the tau operators or / and I have to use the lift operators or it is something related to the data.

I would appreciate the help,

thanks

Miriam RS

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<LAWE_EVP.txt><LAWE.png><LAWE_LBVP.txt>

[Miriam Rodríguez Sánchez]

Hello Geoffrey,

Thank you for your explanation!

I have tried your approximation of the shifted EVP, as well as other definitions of the original EVP (both attached), but they still don’t produce coherent solutions.
Maybe there is something related to the problem construction that I am missing?

Thank you!