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As operating frequencies increase full wave methods such as the finite element method (FEM) become necessary for the analysis of high-frequency circuit structures. Such techniques result in very large systems of equations, and model order reduction (MOR) was proven to be very effective in combating such increased complexity. Using traditional MOR, one has to generate a new reduced model each time a design parameter is modified, thus significantly reducing the CPU efficiency. In this paper, a multidimensional Krylov subspace method is proposed to perform reduction directly on the vector wave equation based FEM system and to generate parametric reduced order models that are valid over the desired parameter range without the need to redo the reduction. In order to accomplish this, second-order Arnoldi methods are extended to include design parameters such as material properties, and geometrical parameters in the reduced order model. In addition, multidimensional moment matching technique is used to address the Krylov incompatibility of FEM problems which include arbitrary frequency dependence in the system. This technique results in significant CPU savings and enables applications such as optimization and design space exploration.
Date of Publication: Feb. 2009