The method of connected local fields for the Helmholtz equation

We show work of the method of connected local fields (CLF) for obtaining semi-analytical solution of the Helmholtz equation. In 2-D case we have the LFE-9 formula and 3-D the LFE-27 formula. Traditionally, it is extremely difficult to solve the Helmholtz equation with finite difference (FD) methods because the required CPU power and memory size is far beyond the capability of the modern computer. However, with the CLF method it becomes possible to model a large-scale problem up to a 100×100 wavelengths in 2D cases or 20×30×30 wavelengths in a cube. We verify the effectiveness of LFE-9 and LFE-27 method by computing the numerical Green´s function.