Adaptive multilevel finite element solution of the Poisson-Boltzmann equation II. Refinement at solvent-accessible surfaces in biomolecular systems

We apply the adaptive multilevel finite element techniques (Holst, Baker, a nd Wang (21)) to the nonlinear Poisson-Boltzmann equation (PBE) in the cont ext of biomolecules; Fast and accurate numerical solution of the PBE in thi s setting is usually difficult to accomplish due to presence of discontinuo us coefficients, delta functions, three spatial dimensions, unbounded domai ns, and rapid (exponential) nonlinearity. However, these adaptive technique s have shown substantial improvement in solution time over conventional uni form-mesh finite difference methods. One important aspect of the adaptive m ultilevel finite element method is the robust a posteriori error estimators necessary to drive the adaptive refinement routines. This article discusse s the choice of solvent accessibility for a posteriori error estimation of PBE solutions and the implementation of such routines in the "Adaptive Pois son-Boltzmann Solver" (APBS) software package based on the "Manifold Code" (MC)libraries. Results are shown for the application of this method to seve ral biomolecular systems. (C) 2000 John Wiley & Sons, Inc.