Review and assessment of interpolatory model order reduction methods for frequency response structural dynamics and acoustics problems

Abstract

SUMMARY Frequency sweeps in structural dynamics, acoustics, and vibro‐acoustics require evaluating frequency response functions for a large number of frequencies. The brute force approach for performing these sweeps leads to the solution of a large number of large‐scale systems of equations. Several methods have been developed for alleviating this computational burden by approximating the frequency response functions. Among these, interpolatory model order reduction methods are perhaps the most successful. This paper reviews this family of approximation methods with particular attention to their applicability to specific classes of frequency response problems and their performance. It also includes novel aspects pertaining to the iterative solution of large‐scale systems of equations in the context of model order reduction and frequency sweeps. All reviewed computational methods are illustrated with realistic, large‐scale structural dynamic, acoustic, and vibro‐acoustic analyses in wide frequency bands. These highlight both the potential of these methods for reducing CPU time and their limitations. Copyright © 2012 John Wiley & Sons, Ltd.

Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: Application to harbor agitation

“…A reduced order model can circumvent this critical di culty, see some previous applications to parameterized Helmholtz equations in [8][9][10][11][12], among others.…”

Model Order Reduction in Structural Dynamics

“…Due to the matching process and the analogy to the Padé approximant those methods are also known as moment matching methods or Padé type methods [9,10]. Here a similar terminology as in [14] was adopted.…”

“…Eq. (5) is equivalent to performed Galerkin projection [14] or applied the least square method to the overestimated system of equations resulting from substituting eq. (3) in eq.…”

Padé approximants and the modal connection: Towards increased robustness for fast parametric sweeps

“…It is only recently that methods have been developed for reduced-order models able to effectively account for general nonpolynomial frequency dependence of the linear system of equations. [19][20][21][22][23][24][25][26][27] They are based on the explicit calculation of the solution vector and its derivatives at a restricted number of main frequencies in the spectrum of interest. In Beattie and Gugercin, 22 these explicit derivatives are used to span a subspace, suitable for a reduced frequency interval in the spectrum, on which the global matrices are projected.…”

“…Alternatively, as done in the present work, these successive frequency-derivative vectors may be used for a component-wise solution expansion via Padé approximants. [19][20][21][23][24][25]28 With this approach, an efficient computation of the solution and its derivatives is performed at a very restricted number of frequencies in the spectrum of interest, which allows to construct Padé approximants for the expansion of the solution in the vicinity of these main frequencies. This alternative, further referred to as the component-wise Padé approximants, additionally offers the possibility to directly target the solution reconstruction for a specific degree-of-freedom (DOF) subset of interest.…”