| Digital filtering structures have recently been applied toward the numerical integration of hyperbolic systems of partial differential equations. Two such methods, the multidimensional wave digital filter (MDWDF) and digital waveguide network (DWN) approaches both rely heavily on electrical network theory, and employ wave variables, which are scattered throughout a grid of scattering junctions. These methods possess many good numerical properties which are carried over from digital filter design; in particular, they are numerically robust in the sense that stability may be maintained even under finite arithmetic conditions. As such, these methods are potentially useful candidates for implementation in special purpose hardware.; In this thesis, the subtext is that such scattering methods can and should be treated as finite difference schemes. In many cases, these methods can be shown to be equivalent to well-known differencing approaches—we pay close attention to the relationship between DWNs and finite difference time domain (FDTD) methods. We make use of this correspondence in order to import (from the finite difference setting) techniques for approaching problems with irregular boundaries, and to examine initialization, boundary conditions, parasitic modes and numerical dispersion properties in detail.; Although these two methods are quite similar in that the main operation, scattering, is the same in either case, conceptually they are very different. A MDWDF is derived from a multidimensional circuit representation of a given system, and as such, the numerical routine is itself a discrete image of the original network. A DWN, however, is usually formulated as collection of lumped scattering junctions which span the problem domain, connected by discrete transmission lines. A useful result is that a DWN can be obtained from a system by the same means as the MDWDF. This unification of the two methods opens the door to a larger class of methods which consist of the same numerically robust basic building blocks.; On the applied side, special attention is paid to problems in beam, plate and shell dynamics. Several simulations are presented. |
