2 research outputs found
An implicit boundary integral method for computing electric potential of macromolecules in solvent
A numerical method using implicit surface representations is proposed to
solve the linearized Poisson-Boltzmann equations that arise in mathematical
models for the electrostatics of molecules in solvent. The proposed method used
an implicit boundary integral formulation to derived a linear system defined on
Cartesian nodes in a narrowband surrounding the closed surface that separate
the molecule and the solvent. The needed implicit surfaces is constructed from
the given atomic description of the molecules, by a sequence of standard level
set algorithms. A fast multipole method is applied to accelerate the solution
of the linear system. A few numerical studies involving some standard test
cases are presented and compared to other existing results.Comment: 28 page
Enriched Gradient Recovery for Interface Solutions of the Poisson-Boltzmann Equation
Accurate calculation of electrostatic potential and gradient on the molecular
surface is highly desirable for the continuum and hybrid modeling of large
scale deformation of biomolecules in solvent. In this article a new numerical
method is proposed to calculate these quantities on the dielectric interface
from the numerical solutions of the Poisson-Boltzmann equation. Our method
reconstructs a potential field locally in the least square sense on the
polynomial basis enriched with Green's functions, the latter characterize the
Coulomb potential induced by charges near the position of reconstruction. This
enrichment resembles the decomposition of electrostatic potential into singular
Coulomb component and the regular reaction field in the Generalized Born
methods. Numerical experiments demonstrate that the enrichment recovery
produces drastically more accurate and stable potential gradients on molecular
surfaces compared to classical recovery techniques