English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

This work further improves the pseudo-transient approach for the PoissonBoltzmann equation (PBE) in the electrostatic analysis of solvatedbiomolecules. The numerical solution of the nonlinear PBE is known to involvemany difficulties, such as exponential nonlinear term, strong singularity bythe source terms, and complex dielectric interface. Recently, a pseudo-timeghost-fluid method (GFM) has been developed in [S. Ahmed Ullah and S. Zhao,Applied Mathematics and Computation, 380, 125267, (2020)], by analyticallyhandling both nonlinearity and singular sources. The GFM interface treatmentnot only captures the discontinuity in the regularized potential and its fluxacross the molecular surface, but also guarantees the stability and efficiencyof the time integration. However, the molecular surface definition based on theMSMS package is known to induce instability in some cases, and a nontrivialLagrangian-to-Eulerian conversion is indispensable for the GFM finitedifference discretization. In this paper, an Eulerian Solvent Excluded Surface(ESES) is implemented to replace the MSMS for defining the dielectricinterface. The electrostatic analysis shows that the ESES free energy is moreaccurate than that of the MSMS, while being free of instability issues.Moreover, this work explores, for the first time in the PBE literature,adaptive time integration techniques for the pseudo-transient simulations. Amajor finding is that the time increment $\Delta t$ should become smaller asthe time increases, in order to maintain the temporal accuracy. This isopposite to the common practice for the steady state convergence, and isbelieved to be due to the PBE nonlinearity and its time splitting treatment.Effective adaptive schemes have been constructed so that the pseudo-time GFMmethods become more efficient than the constant $\Delta t$ ones.

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