Lu, B. Z.; Zhou, Y. C.; Holst, M. J.; McCammon, J. A. Recent progress in numerical methods for the Poisson-Boltzmann equation in biophysical applications. (English) Zbl 1186.92005 Commun. Comput. Phys. 3, No. 5, 973-1009 (2008). Summary: Efficiency and accuracy are two major concerns in numerical solutions of the Poisson-Boltzmann equation for applications in chemistry and biophysics. Recent developments in boundary element, interface, adaptive, finite element methods and other approaches for the Poisson-Boltzmann equation as well as related mesh generation techniques are reviewed. We also discuss challenging problems and possible future work, in particular, for the aim of biophysical applications. Cited in 1 ReviewCited in 77 Documents MSC: 92C05 Biophysics 35Q92 PDEs in connection with biology, chemistry and other natural sciences 65N06 Finite difference methods for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N38 Boundary element methods for boundary value problems involving PDEs 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs Keywords:biomolecular electrostatics; Poisson-Boltzmann equation; adaptive methods; hybrid methods; mesh generation; electrostatic forces Software:APBS; BEMLIB; FFTSVD; UHBD PDFBibTeX XMLCite \textit{B. Z. Lu} et al., Commun. Comput. Phys. 3, No. 5, 973--1009 (2008; Zbl 1186.92005)