The UKAN Computational Acoustics Special Interest Group are pleased to welcome Hadrien Beriot (Siemens) who will present a talk on high-order adaptive finite elements for time-harmonic acoustics applications. This talk will take place on Zoom. Please sign up via Eventbrite here.
In many engineering applications, solutions of the Helmholtz equation are required over a broad frequency range. For acoustics applications, one is often interested in modeling the sound ﬁeld over the full audible frequency range, i.e. from 20 Hz to 20 kHz. The nature of the solution and the requirements in terms of resolution vary drastically over this range. Instead of using a set of increasingly refined meshes, which poses many practical issues, a more efficient computational framework is proposed , which consists in relying on a single mesh resolved with an high-order adaptive finite element approach. When combined with efficient a-priori error indicators, this strategy allows to naturally adjust the resolution across the frequency range to reach a user defined target accuracy. As a side benefit, resorting to p-FEM also allow to circumvent the accumulation of phase errors which hamper the conventional low-order FEM accuracy at mid to high frequencies.
Anisotropic orders may also be introduced to deal eﬃciently with problems involving highly inhomogeneous meshes, with curved and/or high-aspect ratio elements . It may also prove beneficial when the dispersion properties of the waves are direction-dependent, like for instance in the presence of a strong background mean flow. Solutions from several time-harmonic acoustics operators will be presented, including Helmholtz, but also the Biot equations, the Linearized Potential Equations  or the Linearized Euler Equations .
For exterior acoustics applications, p-adaptive FEM may be efficiently combined with an innovative locally-conformal implementation of the Perfectly Matched Layers, applicable on convex domains of general shape . This approach allows to closely surround the scattering objects and in turn to reduce the computational cost. Finally, for large scale applications, parallelization strategies based on optimized Schwarz methods will be discussed .
 Bériot, H., Prinn, A., & Gabard, G. (2016). Efficient implementation of high‐order finite elements for Helmholtz problems. International Journal for Numerical Methods in Engineering, 106(3), 213-240. https://onlinelibrary.wiley.com/doi/full/10.1002/nme.5172
 Bériot, H., & Gabard, G. (2019). Anisotropic adaptivity of the p-FEM for time-harmonic acoustic wave propagation. Journal of Computational Physics, 378, 234-256. https://www.sciencedirect.com/science/article/pii/S0021999118307319
 Gabard, G., Bériot, H., Prinn, A. G., & Kucukcoskun, K. (2018). Adaptive, high-order finite-element method for convected acoustics. AIAA Journal, 56(8), 3179-3191. https://arc.aiaa.org/doi/full/10.2514/1.J057054
 Hamiche, K., Gabard, G., & Bériot, H. (2016). A high-order finite element method for the linearised Euler equations. Acta Acustica united with Acustica, 102(5), 813-823.
 Beriot, H., & Modave, A. (2020). An automatic PML for acoustic finite element simulations with generally-shaped convex domains (2020), accepted for publication in the International Journal for Numerical Methods in Engineering. (preprint: https://hal.archives-ouvertes.fr/hal-02738261/)
 Lieu, A., Marchner, P., Gabard, G., Bériot, H., Antoine, X., & Geuzaine, C. (2020). A non-overlapping Schwarz domain decomposition method with high-order finite elements for flow acoustics. Computer Methods in Applied Mechanics and Engineering, 369, 113223. (preprint: https://hal.archives-ouvertes.fr/hal-02371050/document)