Bériot, Hadrien ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
Antoine, Xavier
Geuzaine, Christophe ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
Language :
English
Title :
A non-overlapping Schwarz domain decomposition method with high-order finite elements for flow acoustics
Publication date :
2020
Journal title :
Computer Methods in Applied Mechanics and Engineering
ISSN :
0045-7825
eISSN :
1879-2138
Publisher :
Elsevier, Amsterdam, Netherlands
Volume :
369
Pages :
113223
Peer reviewed :
Peer Reviewed verified by ORBi
Tags :
CÉCI : Consortium des Équipements de Calcul Intensif Tier-1 supercomputer
Funding text :
This work was performed as part of the CRANE project (Community and Ramp Aircraft NoisE, https://cordis.eur
opa.eu/project/id/606844) funded by the European Union under the Seventh Framework Programme (Grant 606844)
and under the CIFRE contract No 2018/1845 funded by Siemens Industry Software SAS and Association Nationale
de la Recherche et de la Technologie (ANRT). This research was also funded in part through the ARC grant for
Concerted Research Actions (ARC WAVES 15/19-03), financed by the Wallonia-Brussels Federation of Belgium.
The authors acknowledge the use of the computational resources provided by the Consortium des ´ Equipements de Calcul Intensif (C ´ ECI), funded by the Fonds de la Recherche Scientifique de Belgique (F.R.S.-FNRS) under Grant No. 2.5020.11 and by the Walloon Region. The authors would like to thank Prof. Franc¸ois-Xavier Roux for his helpful guidance on non-overlapping Schwarz domain decomposition methods.
Astley, R., Numerical methods for noise propagation in moving flows, with application to turbofan engines. Acoust. Sci. Technol. 30:4 (2009), 227–239.
Farhat, C., Roux, F.-X., A method of finite element tearing and interconnecting and its parallel solution algorithm. Internat. J. Numer. Methods Engrg. 32:6 (1991), 1205–1227.
Gander, M., Magoules, F., Nataf, F., Optimized Schwarz methods without overlap for the Helmholtz equation. SIAM J. Sci. Comput. 24:1 (2002), 38–60.
Boubendir, Y., Antoine, X., Geuzaine, C., A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation. J. Comput. Phys. 231:2 (2012), 262–280.
Thierry, B., Vion, A., Tournier, S., El Bouajaji, M., Colignon, D., Marsic, N., Antoine, X., Geuzaine, C., GetDDM: An open framework for testing optimized Schwarz methods for time-harmonic wave problems. Comput. Phys. Comm. 203 (2016), 309–330.
Dolean, V., Gander, M.J., Gerardo-Giorda, L., Optimized Schwarz methods for Maxwell's equations. SIAM J. Sci. Comput. 31:3 (2009), 2193–2213.
El Bouajaji, M., Thierry, B., Antoine, X., Geuzaine, C., A quasi-optimal domain decomposition algorithm for the time-harmonic Maxwell's equations. J. Comput. Phys. 294 (2015), 38–57.
Rawat, V., Lee, J.-F., Nonoverlapping domain decomposition with second order transmission condition for the time-harmonic Maxwell's equations. SIAM J. Sci. Comput. 32:6 (2010), 3584–3603.
Farhat, C., Macedo, A., Lesoinne, M., Roux, F.-X., Magoulés, F., de La Bourdonnaie, A., Two-level domain decomposition methods with Lagrange multipliers for the fast iterative solution of acoustic scattering problems. Comput. Methods Appl. Mech. Engrg. 184:2–4 (2000), 213–239.
Després, B., Décomposition de domaine et problème de Helmholtz. C. R. Math. Acad. Sci. Paris 1:6 (1990), 313–316.
Myers, M., On the acoustic boundary condition in the presence of flow. J. Sound Vib. 71:3 (1980), 429–434.
Bermúdez, A., Hervella-Nieto, L., Prieto, A., et al. An optimal perfectly matched layer with unbounded absorbing function for time-harmonic acoustic scattering problems. J. Comput. Phys. 223:2 (2007), 469–488.
Bermúdez, A., Hervella-Nieto, L., Prieto, A., Rodríguez, R., Perfectly matched layers. Marburg, S., Nolte, B., (eds.) Computational Acoustics of Noise Propagation in Fluids – Finite and Boundary Element Methods, 2008, Springer, 167–196.
Dolean, V., Jolivet, P., Nataf, F., An Introduction to Domain Decomposition Methods: Algorithms, Theory, and Parallel Implementation, Vol. 144. 2015, SIAM.
Lions, P.-L., On the Schwarz alternating method. III: a variant for nonoverlapping subdomains. Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, Vol. 6, 1990, SIAM Philadelphia, PA, 202–223.
Gander, M., Optimized Schwarz methods. SIAM J. Numer. Anal. 44:2 (2006), 699–731.
Antoine, X., Barucq, H., Bendali, A., Bayliss–Turkel-like radiation conditions on surfaces of arbitrary shape. J. Math. Anal. Appl. 229:1 (1999), 184–211.
Milinazzo, F.A., Zala, C.A., Brooke, G.H., Rational square-root approximations for parabolic equation algorithms. J. Acoust. Soc. Am. 101:2 (1997), 760–766.
Modave, A., Royer, A., Antoine, X., Geuzaine, C., An optimized Schwarz domain decomposition method with cross-point treatment for time-harmonic acoustic scattering. 2020 Preprint HAL-02432422.
Saad, Y., Iterative Methods for Sparse Linear Systems. 2003, Society for Industrial and Applied Mathematics.
Bériot, H., Prinn, A., Gabard, G., Efficient implementation of high-order finite elements for Helmholtz problems. Internat. J. Numer. Methods Engrg. 106:3 (2016), 213–240.
Gabard, G., Bériot, H., Prinn, A., Kucukcoskun, K., Adaptive, high-order finite-element method for convected acoustics. AIAA J. 56:8 (2018), 3179–3191.
Šolín, P., Segeth, K., Doležel, I., Higher-Order Finite Element Methods. 2003, Chapman & Hall, New York.
Amestoy, P.R., Duff, I.S., Koster, J., L'Excellent, J.-Y., A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Anal. Appl. 23:1 (2001), 15–41.
Amestoy, P.R., Guermouche, A., L'Excellent, J.-Y., Pralet, S., Hybrid scheduling for the parallel solution of linear systems. Parallel Comput. 32:2 (2006), 136–156.
Prinn, A., Efficient Finite Element Methods for Aircraft Engine Noise Prediction. (Ph.D. thesis), 2014, University of Southampton.
Bécache, E., Dhia, A.-B., Legendre, G., Perfectly matched layers for the convected Helmholtz equation. SIAM J. Numer. Anal. 42:1 (2004), 409–433.
Marchner, P., Beriot, H., Antoine, X., Geuzaine, C., Stable perfectly matched layers with Lorentz transformation for the convected Helmholtz equation. 2020 Preprint HAL-02556182.
Nataf, F., A new approach to perfectly matched layers for the linearized Euler system. J. Comput. Phys. 214:2 (2006), 757–772.
Karypis, G., Kumar, V., A fast and highly quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20:1 (1999), 359–392.
Bériot, H., Gabard, G., Perrey-Debain, E., Analysis of high-order finite elements for convected wave propagation. Internat. J. Numer. Methods Engrg. 96:11 (2013), 665–688.
Bonazzoli, M., Dolean, V., Graham, I.G., Spence, E.A., Tournier, P.-H., Two-level preconditioners for the Helmholtz equation. International Conference on Domain Decomposition Methods, 2017, Springer, 139–147.
Graham, I., Spence, E., Vainikko, E., Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption. Math. Comp. 86:307 (2017), 2089–2127.
Vion, A., Geuzaine, C., Double sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem. J. Comput. Phys. 266 (2014), 171–190.
Vion, A., Geuzaine, C., Improved sweeping preconditioners for domain decomposition algorithms applied to time-harmonic Helmholtz and Maxwell problems. ESAIM Proc. Surv. 61 (2018), 93–111.
Taus, M., Zepeda-Núñez, L., Hewett, R.J., Demanet, L., L-Sweeps: A scalable, parallel preconditioner for the high-frequency Helmholtz equation. 2019 arXiv preprint arXiv:1909.01467.
Gander, M.J., Zhang, H., A class of iterative solvers for the Helmholtz equation: Factorizations, sweeping preconditioners, source transfer, single layer potentials, polarized traces, and optimized Schwarz methods. SIAM Rev. 61:1 (2019), 3–76.
Mustafi, P., Improved Turbofan Intake Liner Design and Optimization. (Ph.D. thesis), 2013, University of Southampton.
Bériot, H., Gabard, G., Anisotropic adaptivity of the p-FEM for time-harmonic acoustic wave propagation. J. Comput. Phys. 378 (2019), 234–256.
