# Current distribution problem

**URL:** <https://community.freefem.org/t/current-distribution-problem/3751>\
**Category:** General Discussion\
**Created:** [February 15, 2025, 5:11am UTC](https://community.freefem.org/t/current-distribution-problem/3751 "2025-02-15T05:11:13Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Polina](https://avatars.discourse-cdn.com/v4/letter/p/71e660/32.png) [@Polina](https://community.freefem.org/u/Polina)\
**Post date:** [February 15, 2025, 5:11am UTC](https://community.freefem.org/t/current-distribution-problem/3751/1 "2025-02-15T05:11:13Z")

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Hello everyone! I want to simulate the current distribution. I use the continuity equation and the Neumann boundary conditions.

 ![image](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/8/82369fdea31d8b9b9cc23e187c55299bfcfa97a1.png)

The current is set at the boundary as a function of potential. However, the task diverges as soon as the total current is not zero. What condition needs to be added to fix the sum of the currents?

```
(abs(int1d(Th, 1)(ISteel) + int1d(Th, 2)(IMg)) < 1e-1)

func ISteel = 14225 * (-phi)^6 + 93891 * (-phi)^5 + 249128 * (-phi)^4 + 341543 * (-phi)^3 + 255613 * (-phi)^2 + 99090 * (-phi) + 15552;
func IMg = -1764.2 * (-phi)^4 - 10108 * (-phi)^3 - 20773 * (-phi)^2 - 17653 * (-phi) - 4910.6; 

problem Current(phi, v) =  
  int2d(Th)(Sigma * grad(phi)' * grad(v)) 
  - int1d(Th, 1)(ISteel * v)
  - int1d(Th, 2)(IMg * v);

```

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<div class="post-metadata">

**Author:** ![fb77](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/fb77/32/3796_2.png) [@fb77](https://community.freefem.org/u/fb77)\
**Post date:** [February 15, 2025, 6:28pm UTC](https://community.freefem.org/t/current-distribution-problem/3751/2 "2025-02-15T18:28:07Z")

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Hello,  
About your nonlinear equation, it is well-posed if f (or both f on the two pieces of boundary) is increasing in the range of \phi that you expect. Then it can be solved by the Newton method. If f is not everywhere increasing, it does not mean that the problem is ill-posed, but it could be difficult to find a stable scheme to solve it. Eventually you could add to f a stabilizing term c\*(\phi^{k+1}-\phi^k) where k is the iteration index, and c is a sufficiently large constant (so that c+f'\geq 0), or in the Newton method replace f'(\phi^k) by \max(0,f'(\phi^k)).  
Anyway it seems that if f is ISteel or IMg, the sign is wrong in your `int1d`