A Direct Domain-Decomposition Based Time-Domain Finite-Element Method of Linear Complexity for Simulating Multiscaled Structures in Integrated Circuit Systems

摘要

In this work, a direct domain-decomposition based time-domain finite-element method of linear complexity is developed to overcome the challenge of simulating a wide range of geometrical scales present in an integrated circuit system. Via a set of orthogonal prism vector basis functions, we decompose the entire 3-D system of an integrated circuit problem into 2-D subsystems and then into 1-D subsystems with negligible computational cost. We then further decompose each 1-D subsystem into two domains. One is with conductors and the other is with dielectrics. A direct solution without any iteration is proposed to solve the resultant system in linear complexity. Furthermore, the method allows for the use of different meshes in different domains. Numerical simulations of integrated circuits and package problems have demonstrated the accuracy, linear complexity, and meshing flexibility of the proposed method.