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We propose a new circuit analysis method, namely Semi-Implicit Linear-Centric Analysis (SILCA), for efficient SPICE-accurate transient simulation of deep-submicron VLSI circuits with strong parasitic coupling effects introduced by interconnect lines, common substrate, power/ground networks, etc. SILCA is based on two linear-centric techniques. First, a new semi-implicit iterative numerical integration scheme is developed, which applies dynamic time step control accounting for stiff systems and meanwhile keeps constant equivalent conductance for capacitor/inductor companion models. Its convergence and stability properties are characterized. Second, to achieve constant linearized conductance for nonlinear devices during nonlinear iteration process, a successive variable chord method is introduced as an alternative of the Newton-Raphson method and the rank-one update technique is implemented for fast LU factorization. With these techniques, SILCA reduces the number and cost of required LU factorizations dramatically. Experimental results on substrate and power/ground networks have demonstrated that SILCA yields SPICE-like accuracy with an over 80X reduction in LU factorization cost, and an about 20X overall CPU time speedup over SPICE3 for circuits with tens of thousands elements, and the efficiency increases further with the size of a circuit.