Weak boundary treatment for high-order transient analysis of MTLs

This paper presents an innovative treatment of the boundary conditions for the transient simulation of arbitrary interconnects with high-order and/or wavelet-based adaptive schemes. These can be shown to provide better accuracy and less dispersion than standard FDTD schemes. A weak treatment of the boundary conditions allows one to prove explicitly the strict (late time) stability of the discretized system, while preserving high-order accuracy also at the boundaries. This procedure can be applied to the discretization and simulation of possibly complex interconnect networks with arbitrary nonlinear and/or dynamic junctions. Results are given for explicit and implicit fourth-order accurate schemes in both space and time.