Improved Boundary Element Methods for Poisson−Boltzmann Electrostatic Potential and Force Calculations

A patch representation differing from the traditional treatments in the boundary element method (BEM) is presented, which we call the constant “node patch” method. Its application to solving the Poisson−Boltzmann equation (PBE) demonstrates considerable improvement in speed compared with the constant element and linear element methods. In addition, for the node-based BEMs, we propose an efficient interpolation method for the calculation of the electrostatic stress tensor and PB force on the solvated molecular surface. This force calculation is simply an O(N) algorithm (N is the number of elements). Moreover, our calculations also show that the geometric factor correction in the boundary integral equations significantly increases the accuracy of the potential solution on the boundary, and thereby the PB force calculation.