A New Family of Regularized Kernels for the Harmonic Oscillator
Provides a new kernel family for N-body simulations, but the improvement is incremental and domain-specific.
The paper introduces a two-parameter family of regularized kernels for N-body simulations, enabling high-order time stepping. Numerical experiments demonstrate improved accuracy over standard kernels.
In this paper, a new two-parameter family of regularized kernels is introduced, suitable for applying high-order time stepping to N-body systems. These high-order kernels are derived by truncating a Taylor expansion of the non-regularized kernel about $(r^2+ε^2)$, generating a sequence of increasingly more accurate kernels. This paper proves the validity of this two-parameter family of regularized kernels, constructs error estimates, and illustrates the benefits of using high-order kernels through numerical experiments.