sarkas.utilities.maths#

Module of mathematical functions.

Functions

betamp(m, p, alpha, kappa)

Calculate the integral of the Yukawa Green's function using scipy.integrate.quad().

correlationfunction(At, Bt)

Calculate the correlation function between \(\mathbf{A}(t)\) and \(\mathbf{B}(t)\) using scipy.signal.correlate()

force_error_analytic_lcl(potential_type, ...)

Calculate the force error from its analytic formula.

force_error_analytic_pp(potential_type, ...)

Calculate the short-range part of the force error from the approximation formula given in [Dharuman et al., 2017].

force_error_approx_pm(kappa, p, h, alpha)

Calculates the PM part of the force error, \(\Delta F_{\rm pm}\), for a given value of the PPPM parameters.

force_error_approx_pppm(potential)

Calculates the force error, \(\Delta F_{\rm pm}\), for the PPPM algorithm using approximations given in [Dharuman et al., 2017].

yukawa_green_function(k, alpha, kappa)

Evaluate the Green's function of Coulomb/Yukawa potential.