V. Membrane Electrostatics. To date, this is the only off-grid method which is also free from artificial boundary conditions on the simulation box. Its accuracy does not deteriorate for point charges near the interface. It is particularly suitable for parallelization. In practice, many stochastic trajectories of these particles are generated according to Brownian dynamics principles.
Additional criteria enable trajectory termination and residual evaluation for the time-integral.
We have solved the linear Poisson-Boltzmann equation for simple planar and spherical discontinuities. We find that the program is more efficient for larger screening, which shortens the trajectory life-time. Similarly, it becomes more efficient in the calculation of self-energies. We plan to further develop this method as a tool for calculating solvation energies. Results will be compared with a three dimensional version of the reversible binding simulation code, under development by Dr. Evgenii Krissinel'.