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DL_MG: a parallel multigrid Poisson and Poisson−Boltzmann solver for electronic structure calculations in vacuum and solution

DL_MG: a parallel multigrid Poisson and Poisson−Boltzmann solver for electronic structure calculations in vacuum and solution
DL_MG: a parallel multigrid Poisson and Poisson−Boltzmann solver for electronic structure calculations in vacuum and solution
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 ∼109 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.
1549-9618
1412-1432
Womack, James C.
ef9e1954-4a38-4e89-bf25-741a0738e85b
Anton, Lucian
da3a4e52-cdd8-45c2-97c0-174cfb6cbc45
Dziedzic, Jacek
8e2fdb55-dade-4ae4-bf1f-a148a89e4383
Hasnip, Phil J.
15fcdab9-2074-4dca-af33-4ae28665934a
Probert, Matt I. J.
379ad59a-dacf-4c90-87b1-30c09d884f0d
Skylaris, Chris-Kriton
8f593d13-3ace-4558-ba08-04e48211af61
Womack, James C.
ef9e1954-4a38-4e89-bf25-741a0738e85b
Anton, Lucian
da3a4e52-cdd8-45c2-97c0-174cfb6cbc45
Dziedzic, Jacek
8e2fdb55-dade-4ae4-bf1f-a148a89e4383
Hasnip, Phil J.
15fcdab9-2074-4dca-af33-4ae28665934a
Probert, Matt I. J.
379ad59a-dacf-4c90-87b1-30c09d884f0d
Skylaris, Chris-Kriton
8f593d13-3ace-4558-ba08-04e48211af61

Womack, James C., Anton, Lucian, Dziedzic, Jacek, Hasnip, Phil J., Probert, Matt I. J. and Skylaris, Chris-Kriton (2018) DL_MG: a parallel multigrid Poisson and Poisson−Boltzmann solver for electronic structure calculations in vacuum and solution. Journal of Chemical Theory and Computation, 1412-1432. (doi:10.1021/acs.jctc.7b01274).

Record type: Article

Abstract

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 ∼109 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.

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Accepted/In Press date: 15 February 2018
e-pub ahead of print date: 15 February 2018
Published date: 15 February 2018

Identifiers

Local EPrints ID: 419158
URI: https://eprints.soton.ac.uk/id/eprint/419158
ISSN: 1549-9618
PURE UUID: 41ca673b-4579-470e-9cce-d66e28e85597
ORCID for James C. Womack: ORCID iD orcid.org/0000-0001-5497-4482
ORCID for Jacek Dziedzic: ORCID iD orcid.org/0000-0003-4786-372X
ORCID for Chris-Kriton Skylaris: ORCID iD orcid.org/0000-0003-0258-3433

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Date deposited: 06 Apr 2018 16:30
Last modified: 14 Mar 2019 01:41

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