A Cartesian FMM-accelerated Galerkin boundary integral Poisson-Boltzmann solver

The Poisson-Boltzmann model is an effective and popular approach for modeling solvated biomolecules in continuum solvent with dissolved electrolytes. In this paper, we report our recent work in developing a Galerkin boundary integral method for solving the linear Poisson-Boltzmann (PB) equation. The solver has combined advantages in accuracy, efficiency, and memory usage as it applies a well-posed boundary integral formulation to circumvent many numerical difficulties associated with the PB equation and uses an O(N) Cartesian Fast Multipole Method (FMM) to accelerate the GMRES iteration. In addition, special numerical treatments such as adaptive FMM order, block diagonal preconditioners, Galerkin discretization, and Duffy's transformation are combined to improve the performance of the solver, which is validated on benchmark Kirkwood's sphere and a series of testing proteins. •Solves the PB model with O(1/N) accuracy on surface discretized with N elements.•Achieves O(N) efficiency in both memory usage and computational cost.•Is numerically coded with C language and open-source accessible.•Can be conveniently interfaced with broad biological applications.