The purpose of the present study is to develop the neutron diffusion solver and neutron noise simulator based on the Boundary Element Method (BEM). The 2-D, 2-G neutron/adjoint diffusion equation and corresponding neutron/adjoint noise equation were solved using the mentioned method. The developed neutron static and noise simulator based on the finite element method gives accurate results when the more number of the elements is used. The motivation of the present research is to use the boundary element method to reduce the computational cost. The boundary element method attempts to use the given boundary conditions to fit boundary values into the integral equation, rather than values throughout the space defined by a partial differential equation.

The results of static calculation were then benchmarked against the valid data for BIBLIS-2D and IAEA-2D benchmark problems. The neutron noise calculation due to the absorber of variable strength neutron noise source was performed using BEM and the Green's function technique. The adjoint of noise equation was also solved using the same method applied to the forward calculation. Comparison of the calculated neutron noise at zero frequency with the results of static calculation, utilizing the result of adjoint noise calculation and qualitative comparison with similar reported results are three different procedures to validate the neutron noise calculation.

The analysis of the results obtained from the BEM shows that the boundary element method alone, or coupled with the finite element method, is ideally suited for the static and neutron noise calculation from both the accuracy and efficiency viewpoints.

本研究的目的是开发基于边界元方法（BEM）的中子扩散求解器和中子噪声模拟器。使用上述方法求解了二维，2-G中子/伴生扩散方程和相应的中子/伴生噪声方程。当使用更多的元素时，基于有限元方法开发的中子静噪模拟器会给出准确的结果。本研究的动机是使用边界元方法来降低计算成本。边界元方法尝试使用给定的 边界条件 将边界值拟合到积分方程中，而不是将整个值由偏微分方程定义的空间拟合。

然后将静态计算结果与BIBLIS-2D和IAEA-2D基准问题的有效数据进行基准比较。使用BEM和格林函数技术对由于变强度中子噪声源的吸收体引起的中子噪声计算进行了计算。噪声方程的伴随问题也使用与前向计算相同的方法求解。利用伴随噪声计算的结果以及与相似报告结果的定性比较，将零频率下计算出的中子噪声与静态计算结果进行比较是验证中子噪声计算的三种不同程序。

从BEM获得的结果的分析表明，从精度和效率的角度来看，单独使用边界元法或与有限元法相结合，都非常适合静态和中子噪声的计算。