Finite Difference Formulas for Neumann Conditions on Irregularly Shaped Boundaries

A method, based on finite element techniques, is described for obtaining finite differences for Neumann conditions on irregularly shaped boundaries. The resultant difference equations may be used in both time-dependent and -independent problems. As an example, the propagation of an elastic surface wave (Rayleigh wave) around a 90° corner is studied. The results of this simulation compare favorably with laboratory experiments.