Aspects of the generation of finite-difference Green's function sequences for arbitrary 3-D cubic lattice points
The robust and speedy evaluation of lattice Green's functions LGFs) is crucial to the effectiveness of finite-difference Green's function diakoptics schemes. We have recently determined a generic recurrence scheme for the construction of scalar LGF sequences at arbitrary points on a 3-D cubic lattice. For this recurrence scheme, proper care must be taken to retain sufficient accuracy. For certain lattice points recurrence breakdown may occur at some discrete instant in time. Fortunately, this breakdown is rare, may be easily repaired, and does not seem to affect the LGF sequence behaviour. However, due to the anomalous wavefield behaviour induced by the discrete lattice, one must take care to work with time-domain signals that are sufficiently band-limited.