  Simulating the static and dynamic properties of semidilute polymer solutions
with Brownian dynamics (BD) requires the computation of a large system of
polymer chains coupled to one another through excluded-volume and hydrodynamic
interactions. In the presence of periodic boundary conditions, long-ranged
hydrodynamic interactions are frequently summed with the Ewald summation
technique. By performing detailed simulations that shed light on the influence
of several tuning parameters involved both in the Ewald summation method, and
in the efficient treatment of Brownian forces, we develop a BD algorithm in
which the computational cost scales as O(N^{1.8}), where N is the number of
monomers in the simulation box. We show that Beenakker's original
implementation of the Ewald sum, which is only valid for systems without bead
overlap, can be modified so that \theta-solutions can be simulated by switching
off excluded-volume interactions. A comparison of the predictions of the radius
of gyration, the end-to-end vector, and the self-diffusion coefficient by BD,
at a range of concentrations, with the hybrid Lattice Boltzmann/Molecular
Dynamics (LB/MD) method shows excellent agreement between the two methods. In
contrast to the situation for dilute solutions, the LB/MD method is shown to be
significantly more computationally efficient than the current implementation of
BD for simulating semidilute solutions. We argue however that further
optimisations should be possible.
