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Solving a Coupled PDE's using FEniCS

0 votes

I am pretty new on FEniCS.and I want to use FEniCS to solve a coupled set of PDE's including 3 different fields. These equations are coupled and should be solved to find three unknowns. I would like to explain my problem briefly.
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Firstly I just want to solve these coupled PDE's in one dimension and then extend it to 2-D. Could you please tell me how I can deal with this problem in FEniCS? I would really appreciate you referring me to a solved example similar to my problem so I can come up with an idea to implement it in FEniCS. Thanks in advance for your time and attention.

asked Apr 1, 2017 by Leo FEniCS Novice (840 points)

How are you going to couple them in time? Solving for the chemical field simultaneously in the three equations or first solve it in the first equation and then use that value in the other two?

Here is the idea:
Chemical and the electrical fields should be solved simultaneously for 2 unknowns:

1- C_alpha
2- Electric potential

And finally the values of C_alpha should be used in the last equation (equation of motion) to find the displacement (u).

I hope I explained it well!

2 Answers

+3 votes
Best answer

To get a working solver for your problem you can use mixed spaces for the fields you're trying to find.

The latest example of their use (for an advection-diffusion-reaction system of equations) is here:

Then to make a faster solver it might be necessary to solve the equations one a time like in this example:
The advantage of this method is that you can tailor a different linear/non-linear solver for each equation

answered Apr 3, 2017 by alexmm FEniCS User (4,240 points)
selected Apr 3, 2017 by Leo
+3 votes

Look into problems with mixed spaces, such as Navier-stokes.

answered Apr 3, 2017 by KristianE FEniCS Expert (12,900 points)