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Root‐finding absorbing boundary condition for anisotropic scalar waves in infinite media
Author(s) -
Lee Jin Ho
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6572
Subject(s) - isotropy , anisotropy , mathematical analysis , boundary value problem , scalar (mathematics) , phase velocity , group velocity , wave propagation , scalar field , physics , boundary (topology) , mathematics , classical mechanics , geometry , optics
A root‐finding absorbing boundary condition (RFABC) for scalar‐wave propagation problems in infinite anisotropic media was developed. Although the phase velocity and the group velocity in isotropic media have the same sign, the sign of the latter can differ from that of the former in anisotropic media. Therefore, a RFABC for anisotropic scalar waves consistent with the group velocity of the considered media is developed, as the velocity is closely related to the direction of energy propagation. The developed boundary condition is shown to satisfy a criterion for an “enough accurate” boundary condition. The well‐posedness of the boundary condition is proven at the continuous level. Its finite‐element formulation, which ensures well‐posedness at a discrete level, is derived, after which it is demonstrated that accurate and stable solutions to the problem of antiplane shear‐wave propagation in an anisotropic elastic waveguide, an example of anisotropic scalar‐wave propagation, can be obtained using the proposed numerical approach.