DL_MG: A Parallel Multigrid Poisson and Poisson–Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution

TY - JOUR

T1 - DL_MG

T2 - A Parallel Multigrid Poisson and Poisson–Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution

AU - Probert, Matthew Ian James

AU - Womack, James

AU - Anton, Lucian

AU - Dziedzic, Jacek

AU - Hasnip, Philip James

AU - Skylaris, Chris-Kriton

N1 - © 2018 American Chemical Society

PY - 2018/2/15

Y1 - 2018/2/15

N2 - The solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential—a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the Poisson equation, featuring nonhomogeneous dielectric permittivities, ionic concentrations with nonlinear dependencies, and diverse boundary conditions. The analytic solutions generally used to solve the Poisson equation in vacuum (or with homogeneous permittivity) are not applicable in these circumstances, and numerical methods must be used. In this work, we present DL_MG, a flexible, scalable, and accurate solver library, developed specifically to tackle the challenges of solving the Poisson equation in modern large-scale electronic structure calculations on parallel computers. Our solver is based on the multigrid approach and uses an iterative high-order defect correction method to improve the accuracy of solutions. Using two chemically relevant model systems, we tested the accuracy and computational performance of DL_MG when solving the generalized Poisson and Poisson–Boltzmann equations, demonstrating excellent agreement with analytic solutions and efficient scaling to ∼10^9 unknowns and 100s of CPU cores. We also applied DL_MG in actual large-scale electronic structure calculations, using the ONETEP linear-scaling electronic structure package to study a 2615 atom protein–ligand complex with routinely available computational resources. In these calculations, the overall execution time with DL_MG was not significantly greater than the time required for calculations using a conventional FFT-based solver.

AB - The solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential—a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the Poisson equation, featuring nonhomogeneous dielectric permittivities, ionic concentrations with nonlinear dependencies, and diverse boundary conditions. The analytic solutions generally used to solve the Poisson equation in vacuum (or with homogeneous permittivity) are not applicable in these circumstances, and numerical methods must be used. In this work, we present DL_MG, a flexible, scalable, and accurate solver library, developed specifically to tackle the challenges of solving the Poisson equation in modern large-scale electronic structure calculations on parallel computers. Our solver is based on the multigrid approach and uses an iterative high-order defect correction method to improve the accuracy of solutions. Using two chemically relevant model systems, we tested the accuracy and computational performance of DL_MG when solving the generalized Poisson and Poisson–Boltzmann equations, demonstrating excellent agreement with analytic solutions and efficient scaling to ∼10^9 unknowns and 100s of CPU cores. We also applied DL_MG in actual large-scale electronic structure calculations, using the ONETEP linear-scaling electronic structure package to study a 2615 atom protein–ligand complex with routinely available computational resources. In these calculations, the overall execution time with DL_MG was not significantly greater than the time required for calculations using a conventional FFT-based solver.

KW - Poisson solver

KW - electronic structure

KW - CASTEP Computer program

U2 - 10.1021/acs.jctc.7b01274

DO - 10.1021/acs.jctc.7b01274

M3 - Article

SN - 1549-9618

VL - 14

SP - 1412

EP - 1432

JO - Journal of chemical theory and computation

JF - Journal of chemical theory and computation

IS - 3

ER -