On developing stable finite element methods for pseudo-time simulation of biomolecular electrostatics
This paper is concerned with solving the Poisson-Boltzmann equation (PBE), a widely used implicit solvent model for the electrostatic analysis of solvated biomolecules. Some challenges of solving the PBE are that the equation has an exponential nonlinearity, complex interfaces between solute and solvent, and singular source terms. This paper develops a novel finite element method (FEM) in the pseudo-time framework for solving the PBE. By changing the time-independent problem into a time-dependent problem, the authors find that such a technique can completely suppress the nonlinear instability through the time splitting implementation. As for the singular charge sources, they investigate both the singular delta function method and the regularized delta function method. Using a body-fitted mesh, they find that the proposed pseudo-time FEM solvers are more accurate than existing pseudo-time finite difference solvers. Numerical results of several benchmark problems and free energy calculations of protein systems are presented to demonstrate the unconditional stability, accuracy, and robustness of the proposed PBE method.
scientific article; zbMATH DE number 6802843
scientific article