Adaptive pseudo-time methods for the Poisson–Boltzmann equation with Eulerian solvent excluded surface

This work further improves the pseudo-transient approach for Poisson Boltzmann equation (PBE) in electrostatic analysis of solvated biomolecules. The numerical solution nonlinear PBE is known to involve many difficulties, such as exponential term, strong singularity by source terms, and complex dielectric interface. Recently, a pseudo-time ghost-fluid method (GFM) has been developed [S. Ahmed Ullah S. Zhao, Applied Mathematics Computation, 380, 125267, (2020)], analytically handling both nonlinearity singular sources. GFM interface treatment not only captures discontinuity regularized potential its flux across molecular surface, but also guarantees stability efficiency time integration. However, surface definition based on MSMS package induce instability some cases, nontrivial Lagrangian-to-Eulerian conversion indispensable finite difference discretization. In this paper, an Eulerian Solvent Excluded Surface (ESES) implemented replace defining shows that ESES free energy more accurate than MSMS, while being issues. Moreover, explores, first literature, adaptive integration techniques simulations. A major finding increment $\Delta t$ should become smaller increases, order maintain temporal accuracy. opposite common practice steady state convergence, believed be due splitting treatment. Effective schemes have constructed so methods efficient constant ones.