The Eldo Premier simulator addresses the primary concern of analog and mixed-signal designers— performance and capacity increase without sacrificing accuracy. Eldo Premier accelerates the transient simulation, in a spectacular way, of large circuits in either pre-layout or post-layout phases by using sophisticated resolution techniques that do not sacrifice accuracy compared to the golden SPICE results. Eldo Premier accelerates both single-thread simulations and multi-thread simulation. The acceleration of single-thread simulation is provided by new algebraic techniques for the resolution of the system of non-linear differential equations that analog simulators must solve. The acceleration of multi-threaded simulations is a consequence of the natively parallel code of the new simulation kernel and its dedicated data structures. These two acceleration factors naturally combine to offer a significant increase in speed over Eldo Classic. The most significant increases are observed for large circuits (typically at least 10K devices or so), that exhibit some degree of hierarchical regularity. Keywords: Eldo Premier, Fast SPICE, circuit simulation, circuit analysis, parallel processing, speed, capacity, accuracy, foundry certified.