A New Smoothing Algorithm and its Application in Gravitational Lensing_

Based on the DWT (discrete wavelet transform) method, we propose a new smoothing algorithm for computing surface densities from 3D numerical simulation samples. To check its effectiveness, we have applied this algorithm to two Monte-Carlo samples of gravitational lens simulation with different mass resolutions, generated from the isothermal ellipsoid model of dark matter halos. The calculated results indicate that this algorithm can reconstruct accurately the surface density distribution of the gravitational lens simulation sample, and that the lens caustics and critical curves derived from the surface densities agree well with the theoretical curves. We have compared the results calculated by using 3 different wavelet bases (Daub4, Daub6 and B-spline 3th), and identified the best one. Without sacrificing its smoothing capability, this algorithm has a very fast computing speed, suitable for later N-body numerical simulations, which require even higher resolutions.