Proper Orthogonal Decomposition Model Order Reduction of nonlinear IC models

Future simulation for nanoelectronics requires that circuit equations can be coupled to electromagnetics, to semiconductor equations, and to heat transfer. The consequence is that one has to deal with large systems. Model Order Reduction (MOR) is a means to speed up simulation of large systems. Existing MOR techniques mostly apply to linear problems and even then they have to be generalized to become applicable to a resulting system of (Partial) Differential-Algebraic Equations (DAEs, PDAES). To make MOR applicable to industrial applications one has to address nonlinearity and parameterization. Here we consider Proper Orthogonal Decomposition (POD) to reduce the system size. An adaption is presented to also reduce the complexity in evaluating functions and Jacobian-matrices. The problem of reducing nonlinear systems can be described as follows. Given a, possibly large-scale, nonlinear time-invariant dynamical system Σ = (g, f ,h,x,u,y, t)