We present a new, efficient and robust method for computing scalar wave propagation for those cases in which Dirichlet boundary conditions play a key role. The algorithm is versatile and it allows to treat reflection, diffraction, waveguiding regime, scattering and free propagation. The analysis is based upon a representation for a slow neutron wavefunction in terms of the incoming wave and integrals, along the boundaries of an unbounded domain, involving a Green's function and certain auxiliary functions (warranting the Dirichlet boundary conditions). The analysis involves Fourier and Hilbert transforms defined only on the boundaries and enables to exploit the detailed advantages of Fast Fourier Transform (FFT) to perform simulations. Our algorithm proves to be highly effective both in terms in running time and memory load, compared to those based on Finite Differences Methods (FDM). Moreover, since the value of the field at each point may be calculated independently, this algorithm allows parallelization in a natural way.

对于狄利克雷边界条件起关键作用的情况，我们提出了一种新的、有效且稳健的方法来计算标量波传播。该算法是通用的，它允许处理反射、衍射、波导机制、散射和自由传播。该分析基于在入射波和积分方面的慢中子波函数的表示，沿着无界域的边界，涉及格林函数和某些辅助函数（保证狄利克雷边界条件）。该分析涉及仅在边界上定义的傅立叶和希尔伯特变换，并且能够利用快速傅立叶变换 (FFT) 的详细优势来执行模拟。我们的算法在运行时间和内存负载方面都被证明是非常有效的，与基于有限差分方法 (FDM) 的方法相比。此外，由于每个点的字段值可以独立计算，该算法允许以自然的方式并行化。