High Order Compact Multigrid Solver for Implicit Solvation Models

Area of Science:

• Computational chemistry
• Electrostatics
• Molecular modeling

Background:

• Continuum solvation models are essential for molecular mechanics and ab initio molecular dynamics.
• Solving the associated electrostatic problem efficiently is computationally demanding.
• Existing methods may face challenges with complex systems or require significant computational resources.

Purpose of the Study:

• To develop and validate a novel multiscale method for solving electrostatic problems in real space.
• To improve the efficiency and robustness of continuum solvation models.
• To enable accurate simulations of molecular systems with enhanced computational speed.

Main Methods:

• Rewriting the Poisson equation as a stationary convection-diffusion equation.
• Discretizing the equation using a fourth-order compact difference scheme on a general mesh.
• Solving the resulting linear system with a parallel multigrid solver, enhanced by iterative recombination and Krylov subspace methods.
• Applying iterative schemes for nonlinear Poisson equations, such as the Poisson-Boltzmann equation.

Main Results:

• Demonstrated good performance of the accelerated multigrid solver on ideal and physical systems.
• Showcased the solver's effectiveness for linear Poisson equations under various boundary conditions.
• Confirmed the applicability to nonlinear Poisson equations with additional iterative schemes.

Conclusions:

• The proposed multiscale method offers an efficient and robust solution for electrostatic problems in molecular simulations.
• This approach enhances the computational speed of continuum solvation models.
• The method is applicable to both linear and nonlinear Poisson equations, broadening its utility in computational chemistry.