| Abstract | Development of fast computational methods to solve thePoisson-Boltzmann equation (PBE) for molecular elec-
trostatics is important because of the central role played
by electrostatic interactions in many biological processes.
The accuracy and stability of the solution to the PBE
is quite sensitive to the boundary layer between the sol-
vent and the solute which defines the solvent-accessible
surface. In this paper, we propose a new interface-
layer-focused PBE solver for efficiently computing the
electrostatic potential for large molecules. Our method
analytically constructs the solvent-accessible surface of
molecules and then builds nested iso-surface layers out-
wards and inwards from the surface using the distance
field around the surface. We then develop a volume sim-
plification algorithm to adaptively adjust the density of
the irregular grid based on the importance to the PBE
solution. We also generalize finite difference methods on
our irregular grids using Taylor series expansions. Our
algorithm achieves about three times speedup in the iter-
ative solution process of PBE, with more accurate results
on an analytical solvable testing case, compared with the
popular optimized DelPhi program. Our approach can
also be applied directly to solve partial differential equa-
tions arising in other application domains.
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