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Efficient mesh refinement for the Poisson-Boltzmann equation with boundary elements.

Vicente Ramm1, Jehanzeb H Chaudhry2, Christopher D Cooper1,3

  • 1Departamento de Ingeniería Mecánica, Universidad Técnica Federico Santa María, Valparaíso, Chile.

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|March 22, 2021
PubMed
Summary
This summary is machine-generated.

We developed goal-oriented error estimates for the Poisson-Boltzmann equation to refine molecular surface meshes. This adaptive mesh refinement significantly reduces numerical error in solvation free energy calculations efficiently.

Keywords:
Poisson-Boltzmannadaptive mesh refinementboundary element methodgoal-oriented adjoint-based error estimationimplicit solvent

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Area of Science:

  • Computational chemistry
  • Molecular modeling
  • Numerical analysis

Background:

  • The Poisson-Boltzmann equation models molecular electrostatics and solvation.
  • Numerical solutions require surface meshes, often for complex geometries.
  • Accurate solvation free energy calculations depend on mesh quality.

Purpose of the Study:

  • To develop goal-oriented error estimates for adaptive mesh refinement (AMR) in Poisson-Boltzmann calculations.
  • To identify and refine mesh elements contributing most to numerical error in solvation free energy.
  • To improve the efficiency and accuracy of surface meshing for molecular solvation studies.

Main Methods:

  • Utilized adjoint-based analyses to create two goal-oriented error estimators.
  • Applied estimators to determine panel contributions to numerical error in solvation free energy.
  • Implemented an AMR scheme to adaptively refine surface meshes based on error estimates.
  • Tested the approach on spherical and realistic molecular geometries.

Main Results:

  • Identified high-error mesh elements in regions of high electrostatic potential.
  • Demonstrated that AMR reduces error by an order of magnitude with <20% mesh increase.
  • Showed AMR is more efficient than uniform refinement for error estimation.
  • Both error estimators performed similarly within the AMR scheme.

Conclusions:

  • Adjoint-based error estimates enable efficient AMR for molecular surface meshes.
  • The developed AMR scheme significantly improves accuracy and efficiency in solvation energy calculations.
  • This work provides a foundation for automatic, optimal mesh generation in electrostatic solvation modeling.