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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...
The lookback boundary Green's function diakoptics (GFD) schemes reported on before act on field quantities at the boundary set of disjoint domains. This seems a logical and desirable property, but induces computational complexities. It is also possible to construct a domain-based GFD lookback scheme, akin to a discrete Green's function method developed by Vazquez and Parini. We discuss these limited...
In Green's function diakoptics, wave-field interactions between disjoint domains in space are described in terms of interacting multi-port subsystems. In addition to integral-equation based Green's function diakoptics for time-harmonic fields, a demonstrably stable discrete space-time Green's function diakoptics scheme has been reported to be effective for proximate regions. For distant regions it...
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