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To efficiently analyze the large-scale interconnect dominant circuits with inductive couplings (mutual inductances), this paper introduces a new state matrix, called VNA, to stamp inverse-inductance elements by replacing inductive-branch current with flux. The state matrix under VNA is diagonal-dominant, sparse, and passive. To further explore the sparsity and hierarchy at the block level, a new matrix-stretching method is introduced to reorder coupled fluxes into a decoupled state matrix with a bordered block diagonal (BBD) structure. A corresponding block-structure-preserved model-order reduction, called BVOR, is developed to preserve the sparsity and hierarchy of the BBD matrix at the block level. This enables us to efficiently build and simulate the macromodel within a SPICE-like circuit simulator. Experiments show that our method achieves up to 7× faster modeling building time, up to 33× faster simulation time, and as much as 67× smaller waveform error compared to SAPOR [a second-order reduction based on nodal analysis (NA)] and PACT (a first-order 2×2 structured reduction based on modified NA).