An Integral-Based Technique (IBT) to Accelerate the Monte-Carlo Radiative Transfer Computation for Supernovae

We present an integral-based technique (IBT) algorithm to accelerate supernova (SN) radiative transfer calculations. The algorithm utilizes ``integral packets'', which are calculated by the path integral of the Monte-Carlo energy packets, to synthesize the observed spectropolarimetric signal at a given viewing direction in a 3-D time-dependent radiative transfer program. Compared to the event-based technique (EBT) proposed by (Bulla et al. 2015), our algorithm significantly reduces the computation time and increases the Monte-Carlo signal-to-noise ratio. Using a 1-D spherical symmetric type Ia supernova (SN Ia) ejecta model DDC10 and its derived 3-D model, the IBT algorithm has successfully passed the verification of: (1) spherical symmetry; (2) mirror symmetry; (3) cross comparison on a 3-D SN model with direct-counting technique (DCT) and EBT. Notably, with our algorithm implemented in the 3-D Monte-Carlo radiative transfer code SEDONA, the computation time is faster than EBT by a factor of $10-30$, and the signal-to-noise (S/N) ratio is better by a factor of $5-10$, with the same number of Monte-Carlo quanta.