Recently, PhD student YANG Xiaolin and his cooperators: WANG Jiancheng, YANG Chuyuan and YUAN Zunli, from Yunnan Observatories of the Chinese Academy of Sciences, developed a new fast code: Lemon (Linear Integral Equations' Monte Carlo Solver Based on Neumann Solution), aims to solve the radiation transfer processes (RTs) precisely. The scheme of the code is based on linear integral equation and its Neumann series solution. Their research paper was published on The Astrophysical Journal Supplement Series.

RTs are the most primary and omnipresent physical processes in the field of astrophysics and play an important role both in theoretical researches and practical observations. To solve RTs, various methods have been proposed, among which the Monte Carlo (MC) method is the most important and widely applied numerical method due to its simplicity yet powerful and remarkable performances in solving the RTs. The conventional MC method (or photon tracing scheme), however, has an intrinsic defect that is the large amount of computations usually produce a result with quit low statics and large variance, since a significant portion of the computational cost are totally wasted.

In order to overcome the defect, YANG Xiaolin and his collaborators propose a new scheme, in which they suggest that the MC method employed to solve the RTs should be built on the integral equation and its Neumann solution rather than photon tracing. Comparing to the conventional MC method, the most prominent advantage of the new scheme is that it can compel the photons to make contributions to the results at each scattering site, which can improve the calculation efficiency and accuracy significantly. As a result, the aforementioned defect is overcome or alleviated in some sense. In addition, the new scheme can treat the RTs with and without polarizations in a unified framework and simplify the computation procedure, if the geometric configuration of the system has an axial or spherical symmetry. Last but not least, the new scheme can be applied directly to solve any linear differential-integral equations with initial or boundary conditions appropriately provided.

Lemon is developed completely on this new scheme and written in FORTRAN 90 language. It is public available and can be downloaded from: https://github.com/yangxiaolinyn/Lemon. At present, Lemon can solve the problems of RTs mainly restricted to flat space-time. To increase the computing speed, Lemon implements the simplest parallel computation by adopting the Message Passing Interface (MPI) scheme.

The validation of Lemon has been verified by reproducing the results of several test problems. By comparison with the former results, one can find that Lemon is characterized by fast speed, flexibility in computational methods, high efficiency and accuracy, etc. These characters promise and guarantee the potential applications of Lemon for the calculations of RTs in the future.

 Contact:

WANG, Jiancheng, Yunnan Observatories, CAS

jcwang@ynao.ac.cn