The acoustic field in non-uniform layers

The numerical solution of field problems with non-uniform media requires fidelity in the conversion of the mathematical description from continuous to discrete followed by efficient and accurate performance of the ensuing calculations. Here, the conversion process into a matrix equation has been accomplished with minimized distortion to the continuous description, by proper selection of the Green function in the kernel. The efficient and accurate computations are carried out by submitting the matrix equation to a transformation that leads directly to a triangular matrix. While the procedure herewith used should be applicable to arbitrary indices of refraction, it is here restricted to simple distributions to ascertain its applicability to oblique wave propagation and to strong wavemedium interaction.