An efficient inductance extraction algorithm for 3-D interconnects with frequency dependent nonlinear magnetic materials

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.