Implementation of transparent sources embedded in acoustic finite-difference time-domain grids

The finite-difference time-domain (FDTD) method is a simple but powerful numerical method which has been used to perform a wide variety of complex simulations. One of the considerations in using this method is modeling the source of the incident field. When the physical source of acoustic energy is located within the FDTD grid it has typically been modeled as a “hard” source for which a source function determines the field at a source node. One drawback of a hard source is that it acts itself as a scatterer. Moreover, its scattering cross section is dictated by the spatial step size within the grid; thus, scattering is independent of the underlying physical size of the source. In this paper a scheme is presented that permits the creation of completely transparent sources. These sources, although more expensive to implement than traditional hard sources, radiate the same field as a hard source, but do not scatter energy.