# Metafor

ULiege - Aerospace & Mechanical Engineering

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doc:user:elements:contact:lag_aug

# Augmented Lagrangian Method

The Augmented Lagrangian method is used to iterate several times over a single time step, to correct contact forces (augmentation) to get a gap $g$ smaller than a given tolerance (defined by the parameters PRECONNORMALGAP and PRECONTANGENTGAP of the ElementProperties). Contact forces at the iteration $i$ are written :

$$F = L_i + k_N\,g$$

where $k_N$ is the penalty and $L_i$ the Lagrangian. For the next augmentation, the predicted Lagrangian is

$$L_{i+1} = L_i + k_N\,g$$

or it is extrapolated. The gap tolerance is defined by the properties of the contact element. This accuracy must be given to activate the method.

Parameters are set by functions associated to metafor.getAugmentedLagrangianManager() :

  alm = metafor.getAugmentedLagrangianManager()
alm.setMaxNbOfIterations(itma)

where

 itma maximal number of augmentations for a given time step (by default equal to 10)