Adaptive strategies for fast frequency sweeps

Purpose – The purpose of this paper is to compare competing adaptive strategies for fast frequency sweeps for driven and waveguide‐mode problems and give recommendations for practical implementations.Design/methodology/approach – The paper first summarizes the theory of adaptive strategies for multi‐point (MP) sweeps and then evaluates the efficiency of such methods by means of numerical examples.Findings – The authors' numerical tests give clear evidence for exponential convergence. In the driven case, highly resonant structures lead to pronounced pre‐asymptotic regions, followed by almost immediate convergence. Bisection and greedy point‐placement methods behave similarly. Incremental indicators are trivial to implement and perform similarly well as residual‐based methods.Research limitations/implications – While the underlying reduction methods can be extended to any kind of affine parameter‐dependence, the numerical tests of this paper are for polynomial parameter‐dependence only.Practical implication...

[1]  Michel Nakhla,et al.  Transient waveform estimation of high-speed MCM networks using complex frequency hopping , 1993, Proceedings 1993 IEEE Multi-Chip Module Conference MCMC-93.

[2]  O. Farle,et al.  An Adaptive Multi-Point Fast Frequency Sweep for Large-Scale Finite Element Models , 2009, IEEE Transactions on Magnetics.

[3]  Eric James Grimme,et al.  Krylov Projection Methods for Model Reduction , 1997 .

[4]  Valentin de la Rubia,et al.  Reliable Fast Frequency Sweep for Microwave Devices via the Reduced-Basis Method , 2009, IEEE Transactions on Microwave Theory and Techniques.

[5]  J. R. Brauer,et al.  Microwave filter analysis using a new 3-D finite-element modal frequency method , 1997 .

[6]  O. Farle,et al.  Finite-element waveguide solvers revisited , 2004, IEEE Transactions on Magnetics.

[7]  Abdullah Atalar,et al.  Pole-zero computation in microwave circuits using multipoint Pade approximation , 1995 .

[8]  J. Stoer,et al.  Introduction to Numerical Analysis , 2002 .

[9]  P. Dooren,et al.  Asymptotic Waveform Evaluation via a Lanczos Method , 1994 .

[10]  A. Patera,et al.  A PRIORI CONVERGENCE OF THE GREEDY ALGORITHM FOR THE PARAMETRIZED REDUCED BASIS METHOD , 2012 .

[11]  O. Farle,et al.  A Model Order Reduction Method for the Finite-Element Simulation of Inhomogeneous Waveguides , 2008, IEEE Transactions on Magnetics.

[12]  F. Arndt,et al.  Rigorous Hybrid-Mode Analysis of the Transition from Rectangular Waveguide to Shielded Dielectric Image Guide , 1985 .

[13]  Wolfgang Dahmen,et al.  Convergence Rates for Greedy Algorithms in Reduced Basis Methods , 2010, SIAM J. Math. Anal..

[14]  Lawrence T. Pileggi,et al.  Asymptotic waveform evaluation for timing analysis , 1990, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[15]  Rodney D. Slone,et al.  Broadband model order reduction of polynomial matrix equations using single‐point well‐conditioned asymptotic waveform evaluation: derivations and theory , 2003 .

[16]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[17]  Zhaojun Bai,et al.  Dimension Reduction of Large-Scale Second-Order Dynamical Systems via a Second-Order Arnoldi Method , 2005, SIAM J. Sci. Comput..

[18]  Jin-Fa Lee,et al.  Hierarchical vector finite elements for analyzing waveguiding structures , 2003 .