Boundary Conditions for the PBE

To solve the Poisson-Boltzmann equation, suitable boundary conditions need to be assigned. When using finite differences, a common approach is to place the system in a cubic grid so as that the ratio between the largest linear dimension of the system and the side of the cube is fixed (say 70%). Then, the potential on cube's faces is assigned according to some asymptotic approximation of the PBE solution. For large systems, increasing the grid volume can be prohibitive or impossible for computational reasons. The unavoidable questions then is, how close can one get to the molecule and still obtain good results? We are developing a technique to get as close to the molecule as possible, saving memory and computational time without affecting accuracy. As part of this work we have already made a numerical solver of the PBE for the GPU architecture with promising results.