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Simulations, Data Analysis and Algorithms

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Table 1 Symbols and definitions for the accuracy parameters of the \(\pmb{\mathrm{P}^{3}\mathrm{T}}\) scheme

From: GPU-enabled particle-particle particle-tree scheme for simulating dense stellar cluster system

α timestep softening. For all runs α = 0.1
γ ratio of inner and outer cutoff radius (\(r_{\mathrm{in}}/r_{\mathrm{cut}}\)). For all runs γ = 0.1
\(\Delta r_{\mathrm{buff}}\) width of the buffer shell. \(\Delta r_{\mathrm{buff}}=3\sigma\Delta t_{\mathrm{soft}}\), as a standard value
\(\Delta t_{\mathrm{soft}}\) timestep of the soft part. \(\Delta t_{\mathrm{soft}}=(1/256)(N/16\mathrm{K})^{-1/3}\), as a standard value
\(\Delta t_{\max}\) maximum timestep of the hard part. \(\Delta t_{\max}=\Delta t_{\mathrm{soft}}/4\), as a standard value
ϵ plummer softening length. ϵ = (4/N), as a standard value
η accuracy parameter for timestep criterion. η = 0.1, as a standard value
\(r_{\mathrm{cut}}\) outer cutoff radius of smooth transition functions W and K. \(r_{\mathrm{cut}}=4\Delta t_{\mathrm{soft}}\), as a standard value
\(r_{\mathrm{in}}\) inner cutoff radius of smooth transition functions W and K (\(r_{\mathrm{in}}=\gamma r_{\mathrm{cut}}\))
θ opening criterion for tree. θ = 0.4, as a standard value
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