Solve a coupled system with different time scales

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Hello,

I am trying to solve a poroelastic problem ( displacements "u_x" and "u_y", and pressure "p") coupled with one more degree of freedom (T), which depends on the displacements (u_x,u_y).

The problem is that the 4dof equation needs a much smaller time than the poroelastic equations to converge, so I should solve the equations on two different time scales. My idea is:

1) Solve the 4dof for a low time increment, setting the values of the poroelasticity (u_x,u_y, p), so I would get a value of Tn+1.
2) Solve the poroelasticity (dofs 1,2,3) with the updated Tn+1 (dof 4) value.
3) Repeat the process

I have tried to do it with the PARTITION command, solving first 1) and then 2), but it seems that the solutions of 1) are not updated in 2) and vice versa. How should I proceed?

Thank you very much,

Beatriz

[Prof. S. Govindjee]

You will need to say a bit more on what you have done.  See http://feap.berkeley.edu/wiki/index.php?title=Partitions for some information on using partitions with one of FEAP's built-in elements.

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Dear Prof. S. Govindjee,

Thanks for your reply.

We have a multicoupled problem with four dofs. The first three dofs require a large time step while the fourth needs a smaller time step.
How could we solve this shortcoming in FEAP?

Thanks,

Beatriz.

[Prof. R.L. Taylor]

FEAP does not support what you want to do.

One possibility is to program a user module that enters the element with an unused isw and updates the dof's.  You will have to make sure that any element array is updated into the global storage location for the equations.  np(40) for the "u" and np(42) for the rates.

Be careful.

[Prof. S. Govindjee]

Perhaps there is a way to do this.
(1) use partitions
(2) time-step your 4th dof many times with a small dt, in its own partition up to a time DT.
(3) switch to the other partition with dof 1-3. Using a user macro perform the DT timestep on these dofs.
(4) go to (2)

Step (3) is the tricky one and will depend on the time integration scheme that you want to use.  It will definitely take some experimentation to try to make this work and it will really depend on how simple/complex your models are (history variables?) and what type of  time integration you are going to use for your dofs.  One thing that may make it a bit more controllable is to not use FEAP's time integrators, rather use your own that are built into the elements kind of like this paper by Romero et al. https://doi.org/10.1016/j.cma.2021.114013 .