Adaptive strategies for fast frequency sweeps

Abstract

PurposeThe 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/approachThe 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.FindingsThe 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/implicationsWhile 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 implicationsThe present paper describes self‐adaptive point‐placement methods and termination criteria to make MP frequency sweeps more efficient and fully automatic.Originality/valueThe paper provides a self‐adaptive strategy that is efficient and easy to implement. Moreover, it demonstrates that exponential convergence rates can be reached in practice.