Thanks for the response. I think this is worth a try. However, as the 
electric field calculation is entirely decoupled from the nonlinear 
currents & heating part, which need to be solved by newton's method, then 
wouldn't it be effective to just once calculate the field and then start 
the newton iterations for only temperature and currents (probably the 
performance can be made the same, but perhaps code readability decreases)? 
And the second thing is that I want a modular code, where you can choose if 
you want to only calculate electric fields and disregard currents & heating 
or calculate both, in this case it would also be good to keep the codes 
separate. So it would be really convenient to have a some kind a fast 
function like "evaluate_gradient_in_quadrature_point(int index)" or 
something similar.

On Saturday, July 30, 2016 at 1:38:06 PM UTC+3, Daniel Arndt wrote:
>
> krei,
>
> If you want to solve different PDEs on different domains that can be 
> discretized by a common mesh, the preferred approach is to use a hp-vector 
> finite element.
> This means that on each of your subdomains all blocks of your finite 
> element but one are of type FENothing.
> You might want to have a look into step-46 for how to do this.
>
> Best,
> Daniel
>

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