A passivity approach to FDTD stability with application to interconnect modeling

Abstract

The application of the Finite Difference Time Domain (FDTD) method to signal and power integrity problems is limited by the large aspect ratio of interconnects and by small skin depth at high frequency, which impose a very fine grid and long simulations. While local grid refinement can be used to overcome this issue, ensuring the stability of the resulting FDTD scheme is not trivial. We present a powerful stability theory for FDTD based on the concept of passivity. The theory is suitable to develop multiresolution FDTD methods with guaranteed stability. A simple and stable subgridding algorithm is derived. Numerical results show its potential for the efficient modeling of skin effect in interconnects.