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Review and assessment of interpolatory model order reduction methods for frequency response structural dynamics and acoustics problems. (English) Zbl 1246.74023
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.

MSC:
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
Software:
MUMPS
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