Tree-cotree splitting enhanced broadband finite-element simulation including lumped circuit elements

This paper reports our recent progress on the study of the tree-cotree splitting (TCS) technique for solving low frequency instability problem in the finite-element full- wave analysis so as to achieve a broadband simulation from high frequencies down to the DC region. In this paper, the tree-cotree splitting is applied with a diagonal scaling to further improve the matrix conditioning so that the frequency samples in our multipoint model order reduction method, the solution space projection (SSP), can be moved down to even lower frequencies. The experiments also show that the tree-cotree splitting makes a preconditioning more effective. Besides, lumped impedance elements are also incorporated into our finite-element full-wave analysis. Modification is made to the associated discretized model as the tree-cotree splitting is applied.