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Analytical Polarizable Continuum Model for Wavelets on NURBS Patches

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Document pages: 29 pages

Abstract: This article concerns the application of wavelet techniques on molecular surfacesconstituted of four-sided patches. The Polarizable Continuum Model,which is governed by the Poisson-Boltzmann equation, is treated by means ofboundary integral equations. The media inside and outside the molecularsurface consist respectively of the solute and the solvent. For a given electricallycharged molecule, the principal unknown is the electrostatic solvationenergy when the permittivity is specified. The wavelet basis functions are constructedon the unit square which are subsequently mapped onto the patchesthat are assumed to be isotropically shaped and to admit similar surface areas.The initial transmission problem is recast as an integral equation in term ofboth the single and the double layers. Domain decomposition preconditionerserves as acceleration of the linear solver of the single layer which is badlyconditioned.

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