Boundary Element Methods for Helmholtz Problems With Weakly Imposed Boundary Conditions

We consider boundary element methods where the Calderón projector is used for the system matrix and boundary conditions are weakly imposed using a particular variational boundary operator designed using techniques from augmented Lagrangian methods. Regardless of the boundary conditions, both the primal trace variable and the flux are approximated. We focus on the imposition of Dirichlet conditions on the Helmholtz equation and extend the analysis of the Laplace problem from Boundary element methods with weakly imposed boundary conditions [Betcke, Burman, and Scroggs, SIAM J. Sci. Comput., 41 (2019), pp. A1357--A1384] to this case. The theory is illustrated by a series of numerical examples.