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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...
We have extended the linear embedding via Green's operators (LEGO) method to the solution of complicated structures comprised of many different penetrable and conducting media. By combining LEGO with the Arnoldi basis functions, we are able to substantially reduce the size of the relevant algebraic system that arises from the application of the Method of Moments. We review the basics of the overall...
We tackle the scattering from a finite dielectric host medium containing a regular arrangement of (metallic or penetrable) inclusions by using the linear embedding via Green's operators method. After “dicing” the structure into “bricks”, we state an integral equation which we turn into a weak form via the Method of Moments (MoM) with subdomain basis functions. Then, to proceed i) we compress the off-diagonal...
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...
Linear embedding via Green's operators (LEGO) [1,2] is a domain decomposition method in which the electromagnetic scattering by an aggregate of Np bodies (immersed in a homogeneous background medium) is tackled by enclosing each object within an arbitrarily-shaped bounded domain T>k (brick), k = 1,... ,Nd (e.g., see Fig. 1). The bricks are characterized electromagnetically by means of scattering...
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