Solving Radiative Transfer Equation Based On Shooting-Parareal Algorithms

In remote sensing studies of the surface of the Earth and planets,it is essential to quickly and accurately quantify the interior of complex media.To simulate the radiation state of the Earth and planetary surfaces,in 1905 Chandrasekhar described the radiation transport equation in a parallel plane medium:(?)The radiative transfer model is used as the basis for the current inversion algorithm to infer the surface structure and composition of the Earth’s planet.When solving the radiation transport equation,the multi-stream approximation method is often adopted,and the more flows,the higher the accuracy.However,due to the difficulty of numerical calculation,the most used is second-rate calculation so far,but the accuracy is not accurate.The focus of this paper is to propose a numerical solution method for solving the radiative transfer equation.In the previous numerical solution,for the sake of simple calculation,the single scattering albedo is taken as a constant,but the physical problem cannot be accurately described.The advantage of the Shooting-Parareal algorithm is that it takes the single-scattering albedo as a function,which can still solve the radiative transfer equation and better describe the physical process.The Parareal parallel algorithm is applied in the solution process to improve the solution speed.The Shooting-Parareal algorithm is as follows:first use the target method.The initial guess of the radiation intensity at different angles is used as the initial value,and the solution problem is transformed from a marginal value problem to a preliminary value problem.For the initial value problem,the Parareal algorithm is used to solve the numerical solution of the radiative transfer equation to see whether the numerical solution of the solved solution meets the terminal constraints,and if not,the initial value is modified by the secant method.Until the constraint is satisfied.In this paper,the terminal constraint condition can be solved by correcting the initial value in four steps by using the Shooting-Parareal algorithm,and the results show that the algorithm can solve the radiative transfer equation of the variable coefficient.