Numerical simulation of semiconductor devices plays a very important role in the design and development of integrated circuits. We have successfully proposed a new level of convergence performance, when truncation parameter alpha = 1, by combining a simplified, decoupled Gummel-like method (DM) equivalent-circuit model and levelized incomplete LU (L-ILU) factorization in simulating arbitrary, planar semiconductor devices. Further, in order to overcome the problem of decoupled method that the boundary of the device's terminal must be connected to a voltage source, we present a partial decoupled equivalent-circuit model (PDM) with levelized incomplete LU factorization. The complementary techniques for enhancing matrix diagonal dominance and helping program convergence are successfully combined to yield an efficient and robust decoupled nonlinear solution method for numerical simulation. It not only saves memory consumption but also can provide an effective matrix solver for mixed-level semiconductor device and circuit simulation. (C) 2004 Elsevier Ltd. All rights reserved.