A new discontinuous Galerkin method for the nonlinear Poisson–Boltzmann equation

A novel discontinuous Galerkin (DG) method is proposed in this letter to solve the three-dimensional (3D) nonlinear Poisson–Boltzmann (PB) equation for the electrostatic analysis of solvated biomolecules. A regularization formulation is employed in constructing the DG method, which decomposes the electrostatic potential into singular, harmonic, and regular components, so that the inaccurate approximation of singular charge sources can be bypassed. Based on a pseudo-transient continuation approach, the nonlinear term of the PB equation is analytically integrated in our DG method, which avoids the nonlinear instability. A nodal based DG variational formulation is introduced to effectively handle the nonsmooth potential owing to a piecewisely-defined dielectric profile. The stability, convergence, and accuracy of the proposed DG method are numerically verified via a benchmark study.