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--- doc:user:elements:contact:lag_aug [2013/07/10 18:14] – joris
+++ doc:user:elements:contact:lag_aug [2016/03/30 15:23] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
+====== 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 =====