How to discretize the differential equations?

[nychiang]

Hi Dr. Cui,

I wonder how the differential equations is solved in Andes, by finite element?
Can we control the discretization?

Cheers,

NY

[cuihantao]

The differential equations in Andes are DAEs, not PDEs. Finite elements is for PDE. The equations in ANDES is solved by simultaneous methods that discretion the DAE into a set of nonlinear algebraic equations. See Prof. Federico Milano’s book. Regards, Hantao Cui

…

On Feb 24, 2022, 4:56 AM -0600, Nai-Yuan Chiang ***@***.***>, wrote: Hi Dr. Cui, I wonder how the differential equations is solved in Andes, by finite element? Can we control the discretization? Cheers, NY — Reply to this email directly, view it on GitHub, or unsubscribe. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[cuihantao]

Here's the implementation for Trapezoidal method: calc_q is to build the residual equation after discretization, and calc_jac is to calculate the corresponding Jacobian.

These two functions rely on other functions in tds.py to calculate the values for the numerical DAE.

https://github.com/cuihantao/andes/blob/b8b9212c0d2fa24f6af81e1fca3df1034470eea4/andes/routines/daeint.py#L207-L234

[nychiang]

Got it! Thanks a lot for your quick response.
Cheers!