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What is a proper way of solving a multibody nonlinear problem?

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Problem Detail: 

I encountered some system of ~5000 random nodes connected by ~8000 non-hookean springs, with ~1300 nodes at the boundary fixed as the "wall", the potential of the springs are of the form $dx*e^{(dx/a)}$ where $a$ is a constant and $dx$ the strain (displacement/original length) of the spring, I am using Monte Carlo method to find the energy-minimized configuration after I performed some "perturbation", say, a simple shear or a isotropic expansion of the whole system.

It seems that the conventional energy minimization schemes such as "steepest Descent", or "simulated annealing" is not working as efficiently here as the case of linear situations, it always fail to converge to a satisfactorily balanced state.

Could someone share your experiences in dealing with such non-linear situations?

Thank you so much!

Asked By : Long Liang
Answered By : Long Liang

OK, I finally fixed this issue, the right thing to do in such non-linear situation is to use simulated annealing. I am implementing a gradient guided simulated annealing, which works pretty efficiently.

Thanks for everyone who gave me suggestions and guidance to the right path!

Have fun (mixed with a lot of frustrations) with modeling!

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