PDE Apps for Acoustic Ducts: A Parametrized Component-to-System Model-Order-Reduction Approach

  • Jonas Ballani
  • Phuong Huynh
  • David Knezevic
  • Loi Nguyen
  • Anthony T. PateraEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


We present an SCRBE PDE App framework for accurate and interactive calculation and visualization of the parametric dependence of the pressure field and associated Quantities of Interest (QoI)—such as impedance and transmission loss—for an extensive family of acoustic duct models. The Static Condensation Reduced Basis Element (SCRBE) partial differential equation (PDE) numerical approach incorporates several principal ingredients: component-to-system model construction, underlying “truth” finite element PDE discretization, (Petrov)-Galerkin projection, static condensation at the component level, parametrized model-order reduction for both the inter-component (port) and intra-component (bubble) degrees of freedom, and offline-online computational decompositions; we emphasize in this paper reduced port spaces and QoI evaluation techniques, especially frequency sweeps, particularly germane to the acoustics context. A PDE App constitutes a Web User Interface (WUI) implementation of the online, or deployed, stage of the SCRBE approximation for a particular parametrized model: User model parameter inputs to the WUI are interpreted by a PDE App Server which then invokes a parallel cloud-based SCRBE Online Computation Server for calculation of the pressure and associated QoI; the Online Computation Server then downloads the spatial field and scalar outputs (as a function of frequency) to the PDE App Server for interrogation and visualization in the WUI by the User. We present several examples of acoustic-duct PDE Apps: the exponential horn, the expansion chamber, and the toroidal bend; in each case we verify accuracy, demonstrate capabilities, and assess computational performance.



We thank Professor Masayuki Yano of University of Toronto for his contributions to the formulation and verification of the PDE Apps, Dr Sylvain Vallaghé of Akselos for his generous assistance in the FE verification of SCRBE resonances, Professor Kathrin Smetana of the University of Twente for valuable discussions related to the transfer eigenproblem, Professor Peter Dahl of University of Washington and Professor Jer-Ming Chen of Singapore University of Technology and Design (SUTD) for insightful reviews of earlier acoustic PDE Apps, Thomas Leurent of Akselos for his strong support of PDE Apps for education, and Thuc Nguyen of Akselos for his contributions to the web platform. This work was supported by the Swiss Confederations Innovation Promotion Agency (CTI) under Grant 17802.1 PFIW-IW (JB), ONR Contracts N00014-11-1-0713 and N00014-17-1-2077, OSD/AFOSR Grant FA9550-09-0613, SUTD International Design Center, and an MIT Ford Professorship (ATP).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Jonas Ballani
    • 1
  • Phuong Huynh
    • 2
  • David Knezevic
    • 2
  • Loi Nguyen
    • 2
  • Anthony T. Patera
    • 3
    Email author
  1. 1.Swiss Federal Institute of Technology in LausanneLausanneSwitzerland
  2. 2.Akselos S.A.LausanneSwitzerland
  3. 3.Massachusetts Institute of TechnologyCambridgeUSA

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