Spurious Resonances in Coupled Domain-Boundary Variational Formulations of Transmission Problems in Electromagnetism and Acoustics

References

[1] F. Assous, P. Ciarlet and S. Labrunie, Mathematical Foundations of Computational Electromagnetism, Appl. Math. Sci. 198, Springer, Cham, 2018. 10.1007/978-3-319-70842-3Search in Google Scholar

[2] M. Aurada, M. Feischl, T. Führer, M. Karkulik, J. M. Melenk and D. Praetorius, Classical FEM-BEM coupling methods: Nonlinearities, well-posedness, and adaptivity, Comput. Mech. 51 (2013), no. 4, 399–419. 10.1007/s00466-012-0779-6Search in Google Scholar

[3] H. Brakhage and P. Werner, Über das Dirichletsche Aussenraumproblem für die Helmholtzsche Schwingungsgleichung, Arch. Math. 16 (1965), 325–329. 10.1007/BF01220037Search in Google Scholar

[4] A. Buffa and P. Ciarlet, Jr., On traces for functional spaces related to Maxwell’s equations. I. An integration by parts formula in Lipschitz polyhedra, Math. Methods Appl. Sci. 24 (2001), no. 1, 9–30. 10.1002/1099-1476(20010110)24:1<9::AID-MMA191>3.0.CO;2-2Search in Google Scholar

[5] A. Buffa and P. Ciarlet, Jr., On traces for functional spaces related to Maxwell’s equations. II. Hodge decompositions on the boundary of Lipschitz polyhedra and applications, Math. Methods Appl. Sci. 24 (2001), no. 1, 31–48. 10.1002/1099-1476(20010110)24:1<31::AID-MMA193>3.0.CO;2-XSearch in Google Scholar

[6] A. Buffa, M. Costabel and D. Sheen, On traces for H ⁢ ( curl , Ω ) in Lipschitz domains, J. Math. Anal. Appl. 276 (2002), no. 2, 845–867. 10.1016/S0022-247X(02)00455-9Search in Google Scholar

[7] A. Buffa and R. Hiptmair, Galerkin boundary element methods for electromagnetic scattering, Topics in Computational Wave Propagation, Lect. Notes Comput. Sci. Eng. 31, Springer, Berlin (2003), 83–124. 10.1007/978-3-642-55483-4_3Search in Google Scholar

[8] A. Buffa, R. Hiptmair, T. von Petersdorff and C. Schwab, Boundary element methods for Maxwell transmission problems in Lipschitz domains, Numer. Math. 95 (2003), no. 3, 459–485. 10.1007/s00211-002-0407-zSearch in Google Scholar

[9] W. C. Chew, Vector potential electromagnetics with generalized gauge for inhomogeneous media: Formulation, Progr. Electromagnetics Res. 149 (2014), 69–84. 10.2528/PIER14060904Search in Google Scholar

[10] S. H. Christiansen, Discrete Fredholm properties and convergence estimates for the electric field integral equation, Math. Comp. 73 (2004), no. 245, 143–167. 10.1090/S0025-5718-03-01581-3Search in Google Scholar

[11] X. Claeys and R. Hiptmair, First-kind boundary integral equations for the Hodge–Helmholtz operator, SIAM J. Math. Anal. 51 (2019), no. 1, 197–227. 10.1137/17M1128101Search in Google Scholar

[12] X. Claeys and R. Hiptmair, First-kind Galerkin boundary element methods for the Hodge–Laplacian in three dimensions, Math. Methods Appl. Sci. 43 (2020), no. 8, 4974–4994. 10.1002/mma.6203Search in Google Scholar

[13] D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 3rd ed., Appl. Math. Sci. 93, Springer, New York, 2013. 10.1007/978-1-4614-4942-3Search in Google Scholar

[14] M. Costabel, Symmetric methods for the coupling of finite elements and boundary elements (invited contribution), Boundary Elements IX. Vol. 1 (Stuttgart 1987), Springer, Berlin (1987), 411–420. 10.1007/978-3-662-21908-9_26Search in Google Scholar

[15] M. Costabel, Boundary integral operators on Lipschitz domains: Elementary results, SIAM J. Math. Anal. 19 (1988), no. 3, 613–626. 10.1137/0519043Search in Google Scholar

[16] L. Demkowicz, Asymptotic convergence in finite and boundary element methods. I. Theoretical results, Comput. Math. Appl. 27 (1994), no. 12, 69–84. 10.1016/0898-1221(94)90087-6Search in Google Scholar

[17] C. Hazard and M. Lenoir, On the solution of time-harmonic scattering problems for Maxwell’s equations, SIAM J. Math. Anal. 27 (1996), no. 6, 1597–1630. 10.1137/S0036141094271259Search in Google Scholar

[18] R. Hiptmair, Finite elements in computational electromagnetism, Acta Numer. 11 (2002), 237–339. 10.1017/CBO9780511550140.004Search in Google Scholar

[19] R. Hiptmair, Coupling of finite elements and boundary elements in electromagnetic scattering, SIAM J. Numer. Anal. 41 (2003), no. 3, 919–944. 10.1137/S0036142901397757Search in Google Scholar

[20] R. Hiptmair, Maxwell’s equations: Continuous and discrete, Computational Electromagnetism, Lecture Notes in Math. 2148, Springer, Cham (2015), 1–58. 10.1007/978-3-319-19306-9_1Search in Google Scholar

[21] R. Hiptmair and P. Meury, Stabilized FEM-BEM coupling for Helmholtz transmission problems, SIAM J. Numer. Anal. 44 (2006), no. 5, 2107–2130. 10.1137/050639958Search in Google Scholar

[22] R. Kress, Linear Integral Equations, 3rd ed., Appl. Math. Sci. 82, Springer, New York, 2014. 10.1007/978-1-4614-9593-2Search in Google Scholar

[23] W. McLean, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University, Cambridge, 2000. Search in Google Scholar

[24] P. Monk, Finite Element Methods for Maxwell’s Equations, Numer. Math. Sci. Comput., Oxford University, New York, 2003. 10.1093/acprof:oso/9780198508885.001.0001Search in Google Scholar

[25] J.-C. Nédélec, Acoustic and Electromagnetic Equations, Appl. Math. Sci. 144, Springer, New York, 2001. 10.1007/978-1-4757-4393-7Search in Google Scholar

[26] 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

[27] E. Schulz and R. Hiptmair, Coupled domain-boundary variational formulations for Hodge–Helmholtz operators, Integral Equations Operator Theory 94 (2022), no. 1, Paper No. 7. 10.1007/s00020-022-02684-6Search in Google Scholar PubMed PubMed Central

[28] O. Steinbach, Numerical Approximation Methods for Elliptic Boundary Value Problems, Springer, New York, 2008. 10.1007/978-0-387-68805-3Search in Google Scholar

[29] T. von Petersdorff, Boundary integral equations for mixed Dirichlet, Neumann and transmission problems, Math. Methods Appl. Sci. 11 (1989), no. 2, 185–213. 10.1002/mma.1670110203Search in Google Scholar