Numerical method to solve a spring system

[Ale78]

Hello everyone,
this is my first thread in this comunity.

I explain my problem:

I have a triangle mesh http://en.wikipedia.org/wiki/Triangle_mesh where at every vertex coincide a mass element and on every edge I add a spring.
I would like simulate a deformation model.
My idea derive from this article http://www.ecti-thailand.org/assets/papers/1116_pub_36.pdf.
But in this article I think to understand that this is a dynamic simulation along the time.
What's I need, is that user move handled vertex in a final position, the remain vertex are free vertex and their final position should be calculate in the way that every spring reach equilibrium.
What's numerical method can solve my problem. Maybe a minimization?

 

[jaytech]

Try a finite element method: Wikipedia Page

Basically you divide the system into a mesh (as you have) and add the parts of the mesh to form a solution to the system satisfying its boundary conditions.