Implicit/Explicit, BEM/FEM Coupled Scheme for Acoustic Waves with the Wave Equation in the Second Order Formulation

References

[1] T. Abboud, P. Joly, J. Rodríguez and I. Terrasse, Coupling discontinuous Galerkin methods and retarded potentials for transient wave propagation on unbounded domains, J. Comput. Phys. 230 (2011), no. 15, 5877–5907. 10.1016/j.jcp.2011.03.062Search in Google Scholar

[2] A. Bamberger and T. H. Duong, Formulation variationnelle espace-temps pour le calcul par potentiel retardé de la diffraction d’une onde acoustique. I, Math. Methods Appl. Sci. 8 (1986), no. 3, 405–435. 10.1002/mma.1670080127Search in Google Scholar

[3] A. Bamberger and T. H. Duong, Formulation variationnelle pour le calcul de la diffraction d’une onde acoustique par une surface rigide, Math. Methods Appl. Sci. 8 (1986), no. 4, 598–608. 10.1002/mma.1670080139Search in Google Scholar

[4] L. Banjai, Multistep and multistage convolution quadrature for the wave equation: Algorithms and experiments, SIAM J. Sci. Comput. 32 (2010), no. 5, 2964–2994. 10.1137/090775981Search in Google Scholar

[5] L. Banjai, Time-domain Dirichlet-to-Neumann map and its discretization, IMA J. Numer. Anal. 34 (2014), no. 3, 1136–1155. 10.1093/imanum/drt032Search in Google Scholar

[6] L. Banjai and M. Kachanovska, Fast convolution quadrature for the wave equation in three dimensions, J. Comput. Phys. 279 (2014), 103–126. 10.1016/j.jcp.2014.08.049Search in Google Scholar

[7] L. Banjai, C. Lubich and F.-J. Sayas, Stable numerical coupling of exterior and interior problems for the wave equation, Numer. Math. 129 (2015), no. 4, 611–646. 10.1007/s00211-014-0650-0Search in Google Scholar

[8] L. Banjai and F.-J. Sayas, Integral equation methods for evolutionary PDE, Springer Ser. Comput. Math., Springer, Cham (2022), to appear. 10.1007/978-3-031-13220-9Search in Google Scholar

[9] S. C. Brenner and L. R. Scott, The Mathematical Theory of Finite Element Methods, Texts Appl. Math. 15, Springer, New York, 1994. 10.1007/978-1-4757-4338-8Search in Google Scholar

[10] G. Cohen and S. Pernet, Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations, Sci. Comput., Springer, Dordrecht, 2017. 10.1007/978-94-017-7761-2Search in Google Scholar

[11] M. Costabel and F.-J. Sayas, Time-dependent problems with boundary integral equation method, Encyclopedia of Computational Mechanics Second Edition. Part 2, John Wiley & Sons, New York (2017), 1–24. 10.1002/9781119176817.ecm2022Search in Google Scholar

[12] H. Eruslu and F.-J. Sayas, Polynomially bounded error estimates for trapezoidal rule convolution quadrature, Comput. Math. Appl. 79 (2020), no. 6, 1634–1643. 10.1016/j.camwa.2019.09.020Search in Google Scholar

[13] L. C. Evans, Partial Differential Equations, Grad. Stud.Math. 19, American Mathematical Society, Providence, 1998. Search in Google Scholar

[14] S. Falletta and G. Monegato, An exact non reflecting boundary condition for 2D time-dependent wave equation problems, Wave Motion 51 (2014), no. 1, 168–192. 10.1016/j.wavemoti.2013.06.001Search in Google Scholar

[15] S. Falletta and G. Monegato, Exact non-reflecting boundary condition for 3D time-dependent multiple scattering–multiple source problems, Wave Motion 58 (2015), 281–302. 10.1016/j.wavemoti.2015.06.002Search in Google Scholar

[16] E. Hairer, C. Lubich and M. Schlichte, Fast numerical solution of nonlinear Volterra convolution equations, SIAM J. Sci. Statist. Comput. 6 (1985), no. 3, 532–541. 10.1137/0906037Search in Google Scholar

[17] M. E. Hassell and F.-J. Sayas, A fully discrete BEM-FEM scheme for transient acoustic waves, Comput. Methods Appl. Mech. Engrg. 309 (2016), 106–130. 10.1016/j.cma.2016.05.035Search in Google Scholar

[18] C. Johnson and J.-C. Nédélec, On the coupling of boundary integral and finite element methods, Math. Comp. 35 (1980), no. 152, 1063–1079. 10.1090/S0025-5718-1980-0583487-9Search in Google Scholar

[19] A. R. Laliena and F.-J. Sayas, Theoretical aspects of the application of convolution quadrature to scattering of acoustic waves, Numer. Math. 112 (2009), no. 4, 637–678. 10.1007/s00211-009-0220-zSearch in Google Scholar

[20] C. Lubich, Convolution quadrature and discretized operational calculus. II, Numer. Math. 52 (1988), no. 4, 413–425. 10.1007/BF01462237Search in Google Scholar

[21] C. Lubich, On the multistep time discretization of linear initial-boundary value problems and their boundary integral equations, Numer. Math. 67 (1994), no. 3, 365–389. 10.1007/s002110050033Search in Google Scholar

[22] F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl and M. A. McClain, NIST Digital Library of Mathematical Functions, http://dlmf.nist.gov/,Release1.1.1of2021-03-15. Search in Google Scholar

[23] D. Pölz and M. Schanz, On the space-time discretization of variational retarded potential boundary integral equations, Comput. Math. Appl. 99 (2021), 195–210. 10.1016/j.camwa.2021.08.004Search in Google Scholar

[24] S. A. Sauter and C. Schwab, Boundary Element Methods, Springer Ser. Comput. Math. 39, Springer, Berlin, 2011. 10.1007/978-3-540-68093-2Search in Google Scholar

[25] F.-J. Sayas, Retarded Potentials and Time Domain Boundary Integral Equations, Springer Ser. Comput. Math. 50, Springer, Cham, 2016. 10.1007/978-3-319-26645-9Search in Google Scholar

[26] D. Soares, W. J. Mansur and O. Von Estorff, An efficient time-domain FEM/BEM coupling approach based on FEM implicit Green’s functions and truncation of BEM time convolution process, Comput. Methods Appl. Mech. Engrg. 196 (2007), no. 9, 1816–1826. 10.1016/j.cma.2006.10.001Search in Google Scholar