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High Order Compact Multigrid Solver for Implicit Solvation Models.

Arcesio Castañeda Medina1, Rochus Schmid1

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This study presents a multiscale method to solve electrostatic problems in computational chemistry. The approach efficiently handles continuum solvation models using advanced numerical techniques for faster simulations.

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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.