====== 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 ''[[doc:user:elements:contact:elements|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)  |

===== Augmented Lagrangian Algorithm =====

===== Augmented Lagrangian Material =====

===== Augmented Lagrangian Augmentation Method =====

===== Augmented Lagrangian Criterion =====