Comparison of three-dimensional poisson solution methods for particle-based simulation and inhomogeneous dielectrics

Area of Science:

• Computational physics
• Computational chemistry
• Applied mathematics

Background:

• Particle-based simulations are crucial for modeling complex physical systems.
• Solving Poisson's equation is essential for accurately simulating electrostatic interactions among charged particles.
• The boundary element method (BEM) is a common approach for handling inhomogeneous dielectrics in these simulations.

Purpose of the Study:

• To compare the accuracy and computational speed of two BEM approaches: collocation and qualocation.
• To evaluate their performance with both flat and curved surface elements for discretizing dielectric boundaries.
• To assess their suitability for particle-based simulations, particularly in complex systems like ion channels.

Main Methods:

• Implemented collocation BEM based on D. Boda et al.'s induced-charge computation method.
• Implemented qualocation BEM as described by J. Tausch et al.
• Tested both methods on challenging cases: a dielectric sphere in a different medium and a model ion channel, using flat and curved surface elements.

Main Results:

• Qualocation BEM demonstrated significantly higher accuracy than collocation BEM for calculations using flat surface elements.
• When using curved surface elements, both collocation and qualocation BEMs exhibited comparable accuracy for a similar number of elements.
• Simulating charges in high-dielectric media (e.g., ions in water) proved more challenging for accurate computation than in low-dielectric media.

Conclusions:

• The choice of BEM approach and surface element type impacts solution accuracy and efficiency in particle-based simulations.
• Qualocation BEM offers superior accuracy for flat dielectric boundaries, while curved elements make the methods comparable.
• Accurate simulation of systems with high dielectric constants requires careful consideration of computational methods.