TITLE:
Analytical Polarizable Continuum Model for Wavelets on NURBS Patches
AUTHORS:
Maharavo Randrianarivony
KEYWORDS:
Polarizable Continuum Model, Wavelet, Poisson-Boltzmann, Patch, Electrostatic Solvation, Energy
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.8,
August
15,
2017
ABSTRACT: This article concerns the application of wavelet techniques on molecular surfaces
constituted of four-sided patches. The Polarizable Continuum Model,
which is governed by the Poisson-Boltzmann equation, is treated by means of
boundary integral equations. The media inside and outside the molecular
surface consist respectively of the solute and the solvent. For a given electrically
charged molecule, the principal unknown is the electrostatic solvation
energy when the permittivity is specified. The wavelet basis functions are constructed
on the unit square which are subsequently mapped onto the patches
that are assumed to be isotropically shaped and to admit similar surface areas.
The initial transmission problem is recast as an integral equation in term of
both the single and the double layers. Domain decomposition preconditioner
serves as acceleration of the linear solver of the single layer which is badly
conditioned.