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On local algorithms for electrostatics
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DOI：10.1051/m2an/2026025.png)
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Abstract
En 中文
We study finite-difference approximations of the Poisson-Boltzmann (PB) electrostatic energy functional of ionic concentrations and electric displacements constrained by Gauss' law and the ionic mass conservation, and a class of local algorithms for minimizing the finite-difference discretized such energy functional. We prove that the discrete Boltzmann distributions characterize the finite-difference minimizer and obtain the uniform bounds and optimal error estimates in maximum norm for such a minimizer. The local algorithm is an iteration over all the grid boxes that locally minimizes the energy by updating the concentrations and displacement one grid box at a time, keeping Gauss' law and the mass conservation satisfied. A new local algorithm with a shift is constructed for minimizing the Poisson electrostatic energy (the part of the PB energy without ionic concentrations) with a variable dielectric coefficient. We prove the convergence of these local algorithms and present numerical tests to demonstrate the results of our analysis.
Keywords:
Poisson-Boltzmann
Gauss' law
finite difference
error estimate
local algorithm
convergence
Journal
E
IF:
2.2
Papers:
70
Citations:
0
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