Domain decomposition and multi-scale finite elements for electromagnetic analysis of integrated electronic systems

A finite element methodology is presented for computer-aided analysis and design of the interconnect and power distribution network of integrated, packaged electronic systems. The concept of multi-scale finite elements is introduced to describe the generalization of the traditional finite element, understood as a small finite volume of the computational domain over which the unknown field quantity is approximated in terms of interpolative polynomial functions, to a generalized, electromagnetic behavior-baring, scaleable, mathematical macro-model, which captures the electromagnetic response of a sub-region of the computational domain, in a manner seamlessly compatible with the finite element modeling infrastructure. Such generalized finite elements, combined with a domain decomposition methodology suitable for multi-layered electronic substrate electromagnetic modeling, help enhance the modeling versatility and applicability of finite elements to integrated electronic system modeling.