Boundary Element Methods for Helmholtz Problems With Weakly Imposed Boundary Conditions

We consider boundary element methods where the Calder\'on projector is used for system matrix and conditions are weakly imposed using a particular variational operator designed techniques from augmented Lagrangian methods. Regardless of conditions, both primal trace variable flux approximated. focus on imposition Dirichlet Helmholtz equation, extend analysis Laplace problem \emph{Boundary with conditions} to this case. The theory illustrated by series numerical examples.