Comparison of treecodes for computing electrostatic potentials in charged particle systems with disjoint targets and...

Area of Science:

• Computational physics
• Molecular dynamics
• Electrostatics

Background:

• Computing electrostatic potentials is crucial in molecular simulations.
• Direct summation methods are computationally expensive for large systems (O(MN) operations).
• Efficient algorithms are needed to reduce computational cost.

Purpose of the Study:

• To compare the performance of two tree-based methods against direct summation.
• To evaluate accuracy, CPU run time, and memory usage of particle-cluster and cluster-particle treecodes.
• To determine the optimal treecode based on the relative number of sources and targets.

Main Methods:

• Implementation and comparison of particle-cluster treecode and cluster-particle treecode.
• Utilizing octree partitioning for sources or targets.
• Applying far-field and near-field approximations.
• Benchmarking against direct summation.

Main Results:

• Both treecodes significantly reduce computational cost compared to direct summation.
• Particle-cluster treecode is faster when sources outnumber targets (N > M).
• Cluster-particle treecode is faster when targets outnumber sources (M > N).

Conclusions:

• Tree-based methods provide efficient solutions for electrostatic potential calculations in molecular simulations.
• The choice between particle-cluster and cluster-particle treecodes depends on the system's source-to-target ratio.
• These algorithms are valuable tools for handling large charged particle systems.