This paper presents the first algorithm extracting inductance for interconnects with nonlinear magnetic materials. The algorithm models the nonlinear magnetic characteristics by solving the Landau-Lifshitz-Gilbert equation, and the nonhomogeneous magnetic characteristics by introducing the fictitious magnetic charge. A compact system is established and accelerated by a solenoidal basis method. Experimental results show the error for ignoring the non-linearity of magnetic materials is up to 40%. For linear magnetic materials, our algorithm matches well with previous algorithms, but is 3-4 times faster.