# Relationship between the solution convergence and boundary conditions

## Homework Statement:

I want to solve the non lineaire equation using iterative calculation

## Relevant Equations:

[K]{u}={F}
I create an algorithm that can solve [K]{u}={F} for atomic structure, but the results are not converge
• Do the boundary conditions affect the convergence of the resolution of a system of nonlinear partial equations?
• And how to know if the solution is diverged because of the boundary conditions?

Thank you

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BvU
Homework Helper
2019 Award
I looked at your post and can't make sense of what you write. Could you be a bit more elaborate ? Our telepathic capabilities are rather limited. Perhaps not everybody can immediately understand what you mean with K, u and F.

You experience convergence problems, which is not uncommon (been there, done that thousands of times). The quality of help you get depends on the quality of your description. What equations ? What software ? What algorithm ? What boundary conditions ? What crashes specifically ?

I create an algorithm that can solve
Why ? Aren't there zillions of solvers around aleady ?

I looked at your post and can't make sense of what you write. Could you be a bit more elaborate ? Our telepathic capabilities are rather limited. Perhaps not everybody can immediately understand what you mean with K, u and F.

You experience convergence problems, which is not uncommon (been there, done that thousands of times). The quality of help you get depends on the quality of your description. What equations ? What software ? What algorithm ? What boundary conditions ? What crashes specifically ?

Why ? Aren't there zillions of solvers around aleady ?

This problem is found in finite element method.
In other words, Which of the following causes divergence of results :
- node coordinates
- boundary conditions
What are the tricks used to avoid these problems?

BvU
Homework Helper
2019 Award
Does that answer any of my questions ?
1. What equations ?
2. What software ?
3. What algorithm ?
4. What boundary conditions ?
5. What crashes specifically ?
6. Why develop your own algorithm ? Aren't there zillions of solvers around aleady ?
Asking for tricks is rather futile at this point. It isn't magic, it's math ...

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