Karhunen-Loeve based model order reduction of nonlinear systems

Despite continual advances in computing power and the emergence of very efficient algorithms, rigorous analysis of many electrodynamic devices is still often computationally prohibitive. To help overcome these obstacles, a considerable amount of research into so-called "model order reduction" (MOR) methods has been conducted in both the circuit and electromagnetic communities. Traditionally, nonlinearities are dealt with by partitioning the system into linear and nonlinear sub-blocks, and applying MOR techniques to the linear sub-blocks. In systems where the nonlinearity is distributed, however, this is not possible. A method for accomplishing MOR in such cases is described. The theoretical basis for the method is discussed, choices which must be made in implementation are highlighted, and the analysis of a pulse-compression nonlinear transmission line is carried out to demonstrate the capability of the scheme.