An improved method for partial eigensolution of large structures

Model Reduction by Generalized Falk Method for Efficient Field-Circuit Simulations

“…A projection of the matrix ODE in Eq. ( 6) onto the Lanczos basis vectors yields the following transformed matrix ODE, [27] (see Eq. ( 43) in Appendix A):…”

“…These results were the same for the full model. Using the GFM transformed model of the VRM, 27 the transient simulation time was reduced by 17 times (i.e., the speed-up factor), compared to that of the full two-dimensional thermal model, as documented in Table 6. Remark 4.5 Most published results in the VLSI-CAD literature to demonstrate simulation speed-up have been in the frequency domain, essentially using methods of the Lanczos type based on the moment-matching technique.…”

“…The basic idea is to find a convenient and inexpensive transformation of coordinates to simplify the equations of motion that are easier to solve. The WYD reduction method-sometimes called the Ritz reduction method [27] or Ritz vector method [28]-is based on the direct superposition of Ritz vectors constructed from the spatial distribution of the specified dynamic excitation; the generated Ritz vectors are thus excitation dependent. Another reduction technique called the AWE (Asymptotic Waveform Evaluation) method, a moment-matching technique based on the Padé approximation in [29], was also applied to coupled field-circuit simulation for integrated circuits (ICs) [30].…”