Structural acoustics applications in the medium frequency regime are computationally challenging. One avenue of research pursues higher-order discretization methods that can deliver both accuracy and computational efficiency at smaller mesh resolutions. The Discontinuous Enrichment Method (DEM) is one example which distinguishes itself from competing approaches in the additional information it incorporates in the approximation method. It has shown a significant promise for acoustic and structural acoustic applications and therefore is reviewed here, together with new applications to shell problems. Frequency sweeps, which are almost inevitable in many vibro-acoustic engineering problems, present an additional challenge as they significantly increase the already high computational cost. Therefore, interpolatory model reduction techniques that successfully address this challenge and enable real-time frequency sweep analyses are also discussed in this paper.

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