A new approach to implement absorbing boundary condition in biomolecular electrostatics

Area of Science:

• Computational electrostatics
• Biophysics
• Numerical methods

Background:

• Absorbing boundary conditions (ABCs) are crucial for open field problems in computational physics.
• Bayliss-Turkel (BT) operators are established for electromagnetic scattering but underexplored in biomolecular contexts.
• Finite-element method (FEM) is a versatile numerical technique for solving differential equations.

Purpose of the Study:

• To apply the Bayliss-Turkel absorbing boundary condition (BTABC) within the finite-element method (FEM) framework for biomolecular electrostatics.
• To solve the nonlinear Poisson-Boltzmann equation efficiently using Newton's method.
• To minimize the number of unknowns required for accurate electrostatic calculations.

Main Methods:

• A Galerkin finite-element formulation was employed.
• The Bayliss-Turkel absorbing boundary operator was integrated to handle open field conditions.
• The Sommerfeld radiation condition was mapped from the far-field to the near-field.
• Newton's method was used to solve the nonlinear Poisson-Boltzmann equation.

Main Results:

• The combined BTABC-FEM approach effectively addresses open field problems in biomolecular electrostatics.
• The second-order BT operator achieves acceptable accuracy even with closer artificial boundaries.
• Numerical results demonstrated accuracy comparable to analytical methods with reduced grid density.
• The method converges to the exact solution within discretization error.

Conclusions:

• The BTABC-FEM method offers an efficient and accurate solution for biomolecular electrostatics.
• This novel application of BTABC in biomolecular electrostatics provides a valuable computational tool.
• The approach successfully reduces computational cost while maintaining high accuracy.