Once the geometry and physical properties of the radiation system are determined, the integral equation method based on radiation distribution factor (RDFIEM) can be effectively used to calculate the directional radiation intensity with high resolution. However, there exists an inherent shortcoming of low efficiency for statistical ray sampling since the radiation distribution factors (RDFs) are obtained by reverse Monte Carlo (RMC) method. For overcoming this deficiency, an efficient semi-analytical equation-solving RDFIEM (ES-RDFIEM) method is proposed to solve the RDFs directly. In this paper, the principles and formulas of ES-RDFIEM in 1D radiation system with anisotropic scattering medium are developed in detail. Benefit from that the RDF is only related to the geometry and radiation properties of the medium, it can be assumed that only a certain element n has unit blackbody radiation intensity, while the remaining elements do not emit energy. In this way, a semi-analytical set of linear equations can be constructed to solve the RDF matrix directly. Compared with RMC, multiple cases with different radiative parameters are adopted to examine the performance of ES-RDFIEM. Numerical results show that ES-RDFIEM is in good agreement with RMC in most conditions, especially in isotropic scattering or weak scattering of anisotropic scattering. In addition, ES-RDFIEM can effectively avoid the random errors produced by RMC, making the result of ES-RDFIEM smoother than RMC. More importantly, it only takes a few CPU times for computing all the RDF values by ES-RDFIEM, which is one or two orders of magnitude less than that of RMC, and its computational efficiency is almost independent of the radiation properties, showing an excellent efficiency.

一旦确定了辐射系统的几何形状和物理特性，基于辐射分布因子（RDFIEM）的积分方程法就可以有效地用于高分辨率地计算定向辐射强度。但是，由于放射分布因子（RDF）是通过反向蒙特卡洛（RMC）方法获得的，因此统计射线采样效率低下存在一个固有的缺陷。为了克服这一缺陷，提出了一种有效的半解析方程求解RDFIEM（ES-RDFIEM）方法来直接求解RDF。本文详细研究了具有各向异性散射介质的一维辐射系统中ES-RDFIEM的原理和公式。受益于RDF仅与介质的几何形状和辐射特性有关，ñ具有单位黑体辐射强度，而其余元素不发射能量。这样，可以构造线性方程组的半解析集合来直接求解RDF矩阵。与RMC相比，采用了多种辐射参数不同的情况来检验ES-RDFIEM的性能。数值结果表明，ES-RDFIEM在大多数情况下与RMC吻合良好，尤其是在各向同性散射或各向异性散射的弱散射中。此外，ES-RDFIEM可以有效避免RMC产生的随机错误，从而使ES-RDFIEM的结果比RMC更平滑。更重要的是，通过ES-RDFIEM计算所有RDF值只需花费很少的CPU时间，比RMC少一两个数量级，