References
- Bellis C, Cakoni F, Guzina BB. Nature of the transmission eigenvalue spectrum for elastic bodies. IMA J Appl Math. 2012;78(5):895–923. doi: https://doi.org/10.1093/imamat/hxr070
- Bellis C, Guzina BB. On the existence and uniqueness of a solution to the interior transmission problem for piecewise-homogeneous solids. J Elast. 2010;101(1):29–57. doi: https://doi.org/10.1007/s10659-010-9242-0
- Charalambopoulos A, Kirsch A, Anagnostopoulos KA, et al. The factorization method in inverse elastic scattering from penetrable bodies. Inverse Probl. 2006;23(1):27. doi: https://doi.org/10.1088/0266-5611/23/1/002
- Colton D, Kress R. Inverse acoustic and electromagnetic scattering theory. New York (NY): Springer; 2013. (Applied Mathematical Sciences; Vol. 93).
- Sun J, Zhou A. Finite element methods for eigenvalue problems. Boca Raton (FL): CRC Press; 2017.
- Kleefeld A. A numerical method to compute interior transmission eigenvalues. Inverse Probl. 2013;29(10):104012. doi: https://doi.org/10.1088/0266-5611/29/10/104012
- Cakoni F, Colton D, Haddar H. Inverse scattering theory and transmission eigenvalues. Philadelphia (PA): SIAM; 2016.
- Kirsch A, Lechleiter A. The inside–outside duality for scattering problems by inhomogeneous media. Inverse Probl. 2013;29(10):104011. doi: https://doi.org/10.1088/0266-5611/29/10/104011
- Kleefeld A, Pieronek L. The method of fundamental solutions for computing acoustic interior transmission eigenvalues. Inverse Probl. 2018;34(3):035007. doi: https://doi.org/10.1088/1361-6420/aaa72d
- Kleefeld A, Pieronek L. Computing interior transmission eigenvalues for homogeneous and anisotropic media. Inverse Probl. 2018;34(10):105007. doi: https://doi.org/10.1088/1361-6420/aad7c4
- Lakshtanov E, Vainberg B. Bounds on positive interior transmission eigenvalues. Inverse Probl. 2012;28(10):105005. doi: https://doi.org/10.1088/0266-5611/28/10/105005
- Yang Y, Bi H, Li H, et al. Mixed methods for the Helmholtz transmission eigenvalues. SIAM J Sci Comput. 2016;38(3):A1383–A1403. doi: https://doi.org/10.1137/15M1050756
- Yang Y, Han J, Bi H. Non-conforming finite element methods for transmission eigenvalue problem. Comput Methods Appl Mech Eng. 2016;307:144–163. doi: https://doi.org/10.1016/j.cma.2016.04.021
- Ji X, Li P, Sun J. Computation of transmission eigenvalues for elastic waves. arXiv:180203687. 2018.
- Peters S. The inside–outside duality for elastic scattering problems. Appl Anal. 2017;96(1):48–69. doi: https://doi.org/10.1080/00036811.2016.1210789
- Xi Y, Ji X. A lowest order mixed finite element method for the elastic transmission eigenvalue problem. arXiv:181208514. 2018.
- Xi Y, Ji X, Geng H. A C0IP method of transmission eigenvalues for elastic waves. J Comput Phys. 2018;374:237–248. doi: https://doi.org/10.1016/j.jcp.2018.07.053
- Kupradze VD. Potential methods in the theory of elasticity. Jerusalem: Israel Program for Scientific Translations; 1965.
- Betcke T, Trefethen LN. Reviving the method of particular solutions. SIAM Rev. 2005;47(3):469–491. doi: https://doi.org/10.1137/S0036144503437336
- Blåsten E, Liu H. On vanishing near corners of transmission eigenfunctions. J Funct Anal. 2017;273(11):3616–3632. doi: https://doi.org/10.1016/j.jfa.2017.08.023
- McLean W. Strongly elliptic systems and boundary integral equations. Cambridge: Cambridge University Press; 2000.
- Steinbach O. Numerical approximation methods for elliptic boundary value problems: finite and boundary elements. New York: Springer Science & Business Media; 2008.
- Cakoni F, Colton D, Gintides D. The interior transmission eigenvalue problem. SIAM J Math Anal. 2010;42(6):2912–2921. doi: https://doi.org/10.1137/100793542
- Alves CJ. On the choice of source points in the method of fundamental solutions. Eng Anal Bound Elem. 2009;33(12):1348–1361. doi: https://doi.org/10.1016/j.enganabound.2009.05.007