On the Accuracy of First-Order Numerical Derivatives in Multidimensional Digital Waveguide
Ahmet M. KONDOZ · 2007
Digital waveguide mesh (DWM) models are numeri- cal solvers for the wave equation in N -dimensions. They are used for obtaining the traveling-wave solution in practical acoustical modeling applications. Although unstructured meshes can be used with DWMs, regular mesh topologies are traditionally used due to their implementation simplicity. This paper discusses the accuracy of first-order approximations to numerical derivatives on more general unstructured mesh topologies. The results are applied to structured, regular mesh topologies as used in DWM modeling. A comparison of 2D and 3D DWM topologies with respect to the accuracy of first-order approximations to numerical derivatives is presented.