title: An Adaptive Fast Multipole Boundary Element Method for Poisson-Boltzmann Electrostatics.
abstract: The numerical solution of the Poisson-Boltzmann (PB) equation is a useful but a computationally demanding tool for studying electrostatic solvation effects in chemical and biomolecular systems. Recently, we have described a boundary integral equation-based PB solver accelerated by a new version of the fast multipole method (FMM). The overall algorithm shows an order N complexity in both the computational cost and memory usage. Here, we present an updated version of the solver by using an adaptive FMM for accelerating the convolution type matrix-vector multiplications. The adaptive algorithm, when compared to our previous nonadaptive one, not only significantly improves the performance of the overall memory usage but also remarkably speeds the calculation because of an improved load balancing between the local- and far-field calculations. We have also implemented a node-patch discretization scheme that leads to a reduction of unknowns by a factor of 2 relative to the constant element method without sacrificing accuracy. As a result of these improvements, the new solver makes the PB calculation truly feasible for large-scale biomolecular systems such as a 30S ribosome molecule even on a typical 2008 desktop computer.
authors.affiliation: Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China, Center for Molecular Biophysics, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3250, Department of Chemistry & Biochemistry, Center for Theoretical Biological Physics, Department of Pharmacology, Howard Hughes Medical Institute, University of California, San Diego, California 92093.
authors.forename: Benzhuo
authors.initials: B
authors.lastname: Lu
authors.forename: Xiaolin
authors.initials: X
authors.lastname: Cheng
authors.forename: Jingfang
authors.initials: J
authors.lastname: Huang
authors.forename: J Andrew
authors.initials: JA
authors.lastname: McCammon