Parallel efficiency can be greater than unity
Parallel Computing
The electric potential of a macromolecule in a solvent: A fundamental approach
Journal of Computational Physics
Multigrid solution of the Poisson-Boltzmann equation
Journal of Computational Chemistry
Molecular Modeling and Simulation: An Interdisciplinary Guide
Molecular Modeling and Simulation: An Interdisciplinary Guide
A new version of the fast multipole method for screened Coulomb interactions in three dimensions
Journal of Computational Physics
"New-version-fast-multipole-method" accelerated electrostatic calculations in biomolecular systems
Journal of Computational Physics
A Cartesian treecode for screened coulomb interactions
Journal of Computational Physics
IBM Journal of Research and Development
Multiscale molecular dynamics using the matched interface and boundary method
Journal of Computational Physics
SIAM Journal on Scientific Computing
Hi-index | 31.45 |
In this paper, we present a parallel higher-order boundary integral method to solve the linear Poisson-Boltzmann (PB) equation. In our method, a well-posed boundary integral formulation is used to ensure the fast convergence of Krylov subspace linear solver such as GMRES. The molecular surfaces are first discretized with flat triangles and then converted to curved triangles with the assistance of normal information at vertices. To maintain the desired accuracy, four-point Gauss-Radau quadratures are used on regular triangles and sixteen-point Gauss-Legendre quadratures together with regularization transformations are applied on singular triangles. To speed up our method, we take advantage of the embarrassingly parallel feature of boundary integral formulation, and parallelize the schemes with the message passing interface (MPI) implementation. Numerical tests show significantly improved accuracy and convergence of the proposed higher-order boundary integral Poisson-Boltzmann (HOBI-PB) solver compared with boundary integral PB solver using often-seen centroid collocation on flat triangles. The higher-order accuracy results achieved by present method are important to sensitive solvation analysis of biomolecules, particularly when accurate electrostatic surface potentials are critical in the molecular simulation. In addition, the higher-order boundary integral schemes presented here and their associated parallelization potentially can be applied to solving boundary integral equations in a general sense.