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Low-complexity iterative and direct solvers are developed for the volume integral equation (VIE) based general large-scale electrodynamic analysis. The dense VIE system matrix is first represented by a new cluster-based multilevel low-rank representation. In this representation, all the admissible blocks associated with a single cluster are grouped together and represented by a single low-rank block,...
We develop a method to generate an efficient HSS (Hierarchically Semiseparable) representation of the dense integral operators. In this representation, we ensure the rank of each admissible block to be the minimal one required by accuracy. More important, we successfully diagonalize the coupling matrices, and also make the transfer matrices sparse. As compared to H2- or HSS-representations whose coupling...
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