Abstract
Abstract A particle-cluster treecode based on barycentric Hermite interpolation is presented for fast summation of electrostatic particle interactions in 3D. The interpolation nodes are Chebyshev points of the 2nd kind in each cluster. It is noted that barycentric Hermite interpolation is scale-invariant in a certain sense that promotes the treecode’s efficiency. Numerical results for the Coulomb and screened Coulomb potentials show that the treecode run time scales like O(N log N), where N is the number of particles in the system. The advantage of the barycentric Hermite treecode is demonstrated in comparison with treecodes based on Taylor approximation and barycentric Lagrange interpolation.
Highlights
Electrostatic e ects play an important role in determining biomolecular structure, function, and dynamics [4, 16]
Numerical results for the Coulomb and screened Coulomb potentials show that the treecode run time scales like O(N log N), where N is the number of particles in the system
A treecode based on barycentric Hermite interpolation for electrostatic particle interactions weights (6) can be used for any interval [a, b], as long as the Chebyshev points are adapted to the interval; this is useful in the context of the treecode [27]
Summary
Electrostatic e ects play an important role in determining biomolecular structure, function, and dynamics [4, 16]. Abstract: A particle-cluster treecode based on barycentric Hermite interpolation is presented for fast summation of electrostatic particle interactions in 3D. Numerical results for the Coulomb and screened Coulomb potentials show that the treecode run time scales like O(N log N), where N is the number of particles in the system.
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