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Even for a single circuit, it has become increasingly time consuming to simulate at the SPICE level. However, the situation is getting worse when it comes to simulating thousands of such circuits, where often one circuit is closely related to another. This problem arises in applications such as process-voltage-temperature corner circuit simulation or simulation-in-the-loop circuit optimization. The traditional approach to solving this problem is to repeatedly invoke SPICE simulation on each of those circuits. Such an approach does not exploit the similarity among those circuits and could lead to prohibitively high computational cost. This paper presents a new simulation approach capable of simulating hundreds and thousands of closely related systems with the computational cost comparable to or even less than that of a few simulations, yet with the same simulation accuracy and robustness. The proposed approach is based on the combination of the LU-factorization-based direct method (used to construct preconditioners) and Krylov-subspace-based iterative methods (used to solve circuit equations) to explore the common characteristics shared by a set of closely related systems. The key novelty is a systematic method that uses the fewest direct solving for underlying linearized systems and then solves the rest using Krylov-subspace-based iterative methods, with preconditioners computed from those LU factors. In addition, a method of automatically constructing preconditioners from device equations has been developed based on model compilation and demonstrated on MOS transistor Berkeley short-channel IGFET model (BSIM) models. Several circuit examples are included to show the effectiveness of the proposed approach.