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DL_MG: A Parallel Multigrid Poisson and Poisson–Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution
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 ~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.
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Authors (6)
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James Womack
- University of Southampton School of Chemistry
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Lucian Anton
- Cray U.K. Ltd
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Phil Hasnip
- University of York Department of Physics
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Matt Probert
- University of York Department of Physics
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Chris-Kriton Skylaris
- University of Southampton School of Chemistry
Cite as
Full text
- Publication version
- Accepted or Published Version
- License
- Copyright (2018 American Chemical Society)
Keywords
Details
- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
Journal of Chemical Theory and Computation
no. 14,
edition 3,
pages 1412 - 1432,
ISSN: 1549-9618 - Language:
- English
- Publication year:
- 2018
- Bibliographic description:
- Womack J., Anton L., Dziedzic J., Hasnip P., Probert M., Skylaris C.: DL_MG: A Parallel Multigrid Poisson and Poisson–Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution// Journal of Chemical Theory and Computation. -Vol. 14, iss. 3 (2018), s.1412-1432
- DOI:
- Digital Object Identifier (open in new tab) 10.1021/acs.jctc.7b01274
- Verified by:
- Gdańsk University of Technology
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