http://arxiv.org/abs/2210.07021
In this paper, we present a spherical Fast Multipole Method (sFMM) for ray tracing simulation of gravitational lensing (GL) on a curved sky. The sFMM is a non-trivial extension of the Fast Multiple Method (FMM) to sphere $\mathbb S^2$, and it can accurately solve the Poisson equation with time complexity of $O(N)\log(N)$, where $N$ is the number of particles. It is found that the time complexity of the sFMM is near $O(N)$ and the computational accuracy can reach $10^{-10}$ in our test. In addition, comparing with the Fast Spherical Harmonic Transform (FSHT), the sFMM is not only faster but more accurate, as it has the ability to reserve high frequency component of the density field. These merits make the sFMM an optimum method to simulation the gravitational lensing on a curved sky, which is the case for upcoming large-area sky surveys, such as the Vera Rubin Observatory and the China Space Station Telescope.
X. Suo, X. Kang, C. Wei, et. al.
Fri, 14 Oct 22
56/75
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