Design of micro systems, MEMS or mechatronic systems is dominated by the interaction of effects from different physical domains. One important approach to decrease the number of design cycles significantly is system level modeling and simulation. The main challenges for the efficient use of modeling and simulation are a systematic approach for behavioral modeling, automated model generation as well as powerful simulation frameworks. Especially for the latter flexible handling of different models of computation is crucial.
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 implications - The present paper describes self-adaptive point-placement methods and termination criteria to make MP frequency sweeps more efficient and fully automatic. Originality/value - The 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
We present a model order reduction algorithm for linear time-invariant descriptor systems of arbitrary derivative order that incorporates sensitivity analysis for network parameters in respect to design parameters. It is based on implicit moment matching via rational Krylov subspace methods with adaptive choice of expansion points and number of moments based on an error indicator. Additionally, we demonstrate how parametric reduced order models can be obtained at nearly no extra costs, such that parameter studies are extremely accelerated. The finite element model of a yaw rate sensor MEMS device has been chosen as a numerical example, but our method is also applicable to systems arising in modeling and simulation of electromagnetics, electrical circuits, machine tools, heat conduction and other phenomena
This paper presents an efficient model-order reduction approach for computing fast frequency sweeps of system output sensitivities. The proposed framework allows the use of any projection-based order reduction method and renders the dimension of the reduced model independent of the number of parameters. Moreover, a thorough error analysis is presented which also clarifies the convergence properties of existing methods. A numerical experiment validates the authors' findings
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