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Recent progress in numerical methods for the Poisson-Boltzmann equation in biophysical applications. (English) Zbl 1186.92005

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.

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

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APBS; BEMLIB; FFTSVD; UHBD
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