Patent ID: 6349272
Filing Date: 2002-02-19
Classification: G06F

Abstract:
A method of generating a reduced order model of a system having time varying components, comprising the steps of:generating a plurality of differential equations describing time varying components of a system; deriving a frequency domain representation of the plurality of differential equations describing the time varying components of the system by performing a Fourier transform of the plurality of differential equations; discretizing the frequency domain representation of the plurality of differential equations describing the response of the system; determining an approximation of the discretization of the frequency domain representation of the plurality of differential equations, wherein the approximation is generated by projecting onto a Krylov subspace a matrix derived from the frequency domain representation of the plurality of differential equations; and generating at least one response of said system based on said approximation; wherein the step of generating a plurality of differential equations further comprises determining a polynomial expansion of the plurality of differential equations and determining a plurality of ordered differential equations corresponding to the polynomial expansion of the plurality of differential equations, and the step of deriving a frequency domain representation of the plurality of differential equations comprises determining a plurality of transfer functions representations each corresponding to a plurality of ordered differential equations corresponding to the polynomial expansion of the plurality of differential equations, and the step of determining the approximation comprises sequentially determining a reduced order model for each of the plurality of frequency domain representations, each reduced order model being determined by providing as the input to each order of differential equations the result of the next highest ordered differential equations.