Question about the tridiagonal matrix solution

[jinmuluo]

Hi, @oleson @slevis

I'm wondering if the module biogeophys/TridiagonalMod.F90 is used to solve the matrix Ax = b where x is unknown or Ax = b where b is unknown?
a reference code here.

Algorithm Implementation/Linear Algebra/Tridiagonal matrix algorithm - Wikibooks, open books for an open world

en.wikibooks.org

Best,

Jinmu

 

[oleson]

where x is unknown.

 

[jinmuluo]

where x is unknown.

Hi Keith,

Thank you so much for your quick reply.
I have a follow-up question about the module : soilbiogeochem/SoilBiogeochemLittVertTranspMod.F90
If I understand correctly, what this module wants to do is to build a vertical mixing matrix A which is based on the vertical concentration gradient to update the CN vertical concentration, for example, to predict the vertical mixing of the soil carbon in the next time step, C(t+1) = A*C(t).
Do you think the TridiagonalMod.F90 module satisfies this purpose? If I misunderstood anything, please let me know, I have been stuck here for a while.

Best,

 

[oleson]

I believe so. There isn't documentation in the technical note that documents this approach in detail for vertical mixing of carbon, but something similar is done for soil temperature. See Chapter 6:

Redirecting...

escomp.github.io

In particular, equation 2.6.12 describes the set of equations for soil temperature in which T(n+1) is the soil temperature at the next time step n+1, r is the "forcing term", and a,b,c are the subdiagonal, diagonal, and superdiagonal elements.

 

[jinmuluo]

I believe so. There isn't documentation in the technical note that documents this approach in detail for vertical mixing of carbon, but something similar is done for soil temperature. See Chapter 6:

Redirecting...

escomp.github.io

In particular, equation 2.6.12 describes the set of equations for soil temperature in which T(n+1) is the soil temperature at the next time step n+1, r is the "forcing term", and a,b,c are the subdiagonal, diagonal, and superdiagonal elements.

Hi Keith,

Thank you so much for that, I've now noticed the differences. I guess the Litter transport module also used the Crank-Nicholson method and the alpha is zero in this module (alpha in the formula 2.6.11), the same thing for the soil water module.

Best,

Jinmu