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

TL;DR

This paper introduces a novel Galerkin boundary integral solver for the Poisson-Boltzmann equation that combines Cartesian FMM acceleration with advanced numerical techniques, achieving high accuracy and efficiency for biomolecular simulations.

Contribution

It develops a new boundary integral method with FMM acceleration and specialized numerical treatments, improving the solution of the Poisson-Boltzmann equation for biomolecules.

Findings

Validated on Kirkwood's sphere and proteins.

Achieves O(N) complexity with FMM acceleration.

Demonstrates improved accuracy and efficiency.

Abstract

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 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.