Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast Newton Iterative Method for Local Steric Poisson--Boltzmann
  Theories in Biomolecular Solvation   This work proposes a fast iterative method for local steric
Poisson--Boltzmann (PB) theories, in which the electrostatic potential is
governed by the Poisson's equation and ionic concentrations satisfy equilibrium
conditions. To present the method, we focus on a local steric PB theory derived
from a lattice-gas model, as an example. The advantages of the proposed method
in efficiency lies on a key idea that ionic concentrations as scalar implicit
functions of the electrostatic potential, i.e, generalized Boltzmann
distributions, are numerically available. The existence, uniqueness, boundness,
and smoothness of such distributions are rigorously established. A Newton
iteration method with truncation is proposed to solve a nonlinear system
discretized from the generalized PB equations. The existence and uniqueness of
the solution to the discretized nonlinear system are established by showing
that it is a unique minimizer of a constructed convex energy. Thanks to the
boundness of ionic concentrations, truncation bounds for the potential are
obtained by using the extremum principle. The truncation step in iterations is
shown to be energy, residual, and error decreasing. To further speed-up
computations, we propose a novel precomputing-interpolation strategy, which is
applicable to other local steric PB theories and makes the proposed methods for
solving steric PB theories as efficient as for solving the classical PB theory.
Analysis on the Newton iteration method with truncation shows local quadratic
convergence for the proposed numerical methods. Applications to realistic
biomolecular solvation systems reveal that counterions with steric hindrance
stratify in an order prescribed by the parameter of ionic valence-to-volume
ratio. Finally, we remark that the proposed iterative methods for local steric
PB theories can be readily incorporated in well-known classical PB solvers.

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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat