The role of the direct transfer matrix as a connectivity matrix and application to the helmholtz equation in 2D: Relation to numerical methods and free field radiation example

The Direct Transfer Function (DTF) matrix was developed in the framework of the Global Transfer Direct Transfer (GTDT) method of transmission path analysis. This method aims at solving the problem of transmission paths among subsystems from a general N-dimensional linear network, representing a vibro-acoustical model under study. The DTF matrix can be calculated from the Global Transfer Functions (GTFs), which are measurable quantities, and it is built from all the Direct Transfer Functions (DTFs) between subsystem pairs. The DTFs allow to define transmission paths by relating the signals between two network subsystems when the remaining ones become somehow blocked. In this paper, the role of the DTF matrix as a connectivity matrix is first shown by solving the Helmholtz equation in a two-dimensional grid. The results are compared with those arising from the analysis of the stencils of various numerical methods. Some finite difference and finite element methods have been considered. The connectivity role of the DTF matrix is also elucidated by means of a free field radiation example.