ARGOS: An adaptive refinement goal-oriented solver for the linearized Poisson-Boltzmann equation.

Area of Science:

• Computational Chemistry
• Molecular Modeling
• Scientific Computing

Background:

• Accurate calculation of electrostatic coupling between molecules in solvent is crucial for understanding molecular interactions.
• Existing finite difference solvers (MEAD, APBS) have limitations in precision and computational efficiency.
• The development of advanced numerical methods is needed to overcome these limitations.

Purpose of the Study:

• To develop and test an adaptive finite element solver for electrostatic coupling.
• To introduce a goal-oriented a posteriori error estimate for improved accuracy and efficiency.
• To evaluate the solver's performance against established methods using various molecular systems.

Main Methods:

• Implementation of an adaptive finite element method (FEM) for electrostatic calculations.
• Derivation and integration of a goal-oriented a posteriori error estimator.
• Numerical validation using problems with known analytical solutions and complex biomolecular systems (chromophores, SARS-CoV-2 spike protein/ACE2 receptor).

Main Results:

• The developed FEM solver, ARGOS, demonstrates orders of magnitude improvement in precision compared to finite difference solvers.
• ARGOS achieves significantly shorter computational times.
• Numerical experiments confirm the accuracy and efficiency of ARGOS across different molecular configurations.

Conclusions:

• The novel adaptive FEM solver ARGOS offers a superior approach for calculating electrostatic coupling in molecular systems.
• The goal-oriented error estimate is key to ARGOS's enhanced performance.
• ARGOS presents a powerful tool for molecular modeling, with demonstrated advantages over MEAD and APBS.