Perfectly matched layer technique for the numerical computation of wave propagation phenomena

The original Perfectly Matched Layer (PML) technique is based on splitting the physical quantities in such a manner, that an absorption of waves impinging at any angle onto the boundary is achieved. We obtain the same properties by mapping the solution of the Helmholtz equation from the real coordinate space to a complex coordinate space, e.g. an analytic continuation of the solution. Therewith, we substitute the corresponding (real) partial derivatives with respect to space coordinates by their complex counterparts, which Introduces the correct damping into the system. The proper choice of the damping functions is of great importance, especially in order to obtain a stable and efficient PML method. We show the applicability to real life problems by computing the radiation of an ultrasound array antenna immersed in water.