Strictly Stable High Order Schemes for Transient Analysis of MTL'S

This paper presents a class of high-order difference schemes for the transient simulation of multiconductor interconnects and interconnect networks. These schemes are shown to provide better accuracy and less dispersion than standard FDTD schemes for the analysis of electrically long lines. In particular, a special treatment of the boundary conditions, which are implemented in a weak form for both linear, nonlinear, and dynamic terminations, allows to prove explicitly the strict (late time) stability of the discretized system. High-order accuracy is preserved at the boundaries. Numerical examples are provided for explicit and implicit fourth-order schemes. Finally, the optimization of the schemes through wavelet-based spatial discretizations leading to self-adaptive algorithms is discussed in the general framework.