  We introduce a Monte-Carlo algorithm for the simulation of charged particles
moving in the continuum. Electrostatic interactions are not instantaneous as in
conventional approaches, but are mediated by a constrained, diffusing electric
field on an interpolating lattice. We discuss the theoretical justifications of
the algorithm and show that it efficiently equilibrates model polyelectrolytes
and polar fluids. In order to reduce lattice artifacts that arise from the
interpolation of charges to the grid we implement a local, dynamic subtraction
algorithm. This dynamic scheme is completely general and can also be used with
other Coulomb codes, such as multigrid based methods.
