DL_MG: A Parallel Multigrid Poisson and Poisson-Boltzmann Solver for Electronic Structure Calculations in Vacuum and...

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Mechanics

Background:

• Solving the Poisson equation is essential for determining electrostatic potential in quantum mechanical Hamiltonian.
• Simulating complex electronic structures requires advanced numerical methods for the Poisson equation due to nonhomogeneous environments.
• Analytic solutions are insufficient for complex Poisson equation variants in modern simulations.

Purpose of the Study:

• To introduce DL_MG, a novel, flexible, scalable, and accurate solver library for the Poisson equation.
• To address the challenges of solving complex Poisson equations in large-scale electronic structure calculations on parallel systems.
• To enhance the accuracy and efficiency of electrostatic potential calculations in computational chemistry.

Main Methods:

• Developed DL_MG based on the multigrid approach.
• Implemented an iterative high-order defect correction method for enhanced solution accuracy.
• Tested DL_MG on model systems for generalized Poisson and Poisson-Boltzmann equations, and in large-scale electronic structure calculations using ONETEP.

Main Results:

• DL_MG demonstrated excellent agreement with analytic solutions for model systems.
• The solver exhibited efficient computational performance, scaling to approximately 10^9 unknowns on hundreds of CPU cores.
• DL_MG showed comparable execution times to conventional FFT-based solvers in large-scale protein-ligand complex simulations.

Conclusions:

• DL_MG is a highly accurate and efficient solver for complex Poisson equations in large-scale electronic structure calculations.
• The library provides a scalable solution for modern computational chemistry and materials science challenges.
• DL_MG integrates seamlessly with existing electronic structure packages, offering a viable alternative to traditional methods.