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I am looking for the details of commonly-used predictors for accelerating the convergence of iterations using Newton-Raphson scheme for nonlinear problems in FEM. I am looking specifically for static problems.

Note: Such predictors based on velocity and/or acceleration are used for transient problems but they are not applicable for pure static problems.

Appreciate any inputs.

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  • $\begingroup$ Is it even possible to accelerate convergence of Newton's method? I wasn't aware that that's possible. $\endgroup$ – Wolfgang Bangerth 2 days ago
  • $\begingroup$ @WolfgangBangerth, Yes. If we can compute the initial guess (the predictor) such that it is closer to the actual solution, then the number of iterations certainly decrease. Such an approach also allows us to use bigger load steps. $\endgroup$ – Chenna K 2 days ago
  • $\begingroup$ Sure, but that happens before you even start the Newton iteration. So if I understand you right, you're looking for something that produces a good initial guess from which to start a Newton iteration? I think if so, you will have to explain in more detail what the set up is that you're trying to solve, and what information is available to compute a predictors. $\endgroup$ – Wolfgang Bangerth yesterday

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