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Adaptive multilevel finite element solution of the Poisson–Boltzmann equation II. Refinement at solvent‐accessible surfaces in biomolecular systems
Author(s) -
Baker N.,
Holst M.,
Wang F.
Publication year - 2000
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/1096-987x(20001130)21:15<1343::aid-jcc2>3.0.co;2-k
Subject(s) - finite element method , estimator , a priori and a posteriori , nonlinear system , solver , mathematics , adaptive mesh refinement , computer science , exponential function , polygon mesh , computational science , context (archaeology) , algorithm , mathematical optimization , mathematical analysis , physics , statistics , quantum mechanics , thermodynamics , philosophy , computer graphics (images) , paleontology , epistemology , biology
We apply the adaptive multilevel finite element techniques (Holst, Baker, and Wang 21) to the nonlinear Poisson–Boltzmann equation (PBE) in the context of biomolecules. Fast and accurate numerical solution of the PBE in this setting is usually difficult to accomplish due to presence of discontinuous coefficients, delta functions, three spatial dimensions, unbounded domains, and rapid (exponential) nonlinearity. However, these adaptive techniques have shown substantial improvement in solution time over conventional uniform‐mesh finite difference methods. One important aspect of the adaptive multilevel finite element method is the robust a posteriori error estimators necessary to drive the adaptive refinement routines. This article discusses the choice of solvent accessibility for a posteriori error estimation of PBE solutions and the implementation of such routines in the “Adaptive Poisson–Boltzmann Solver” (APBS) software package based on the “Manifold Code” (MC) libraries. Results are shown for the application of this method to several biomolecular systems. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1343–1352, 2000