Volume 2, Issue 2
Asymptotic Radiation Conditions for Reduced Wave Equation

Kang Feng

DOI:

J. Comp. Math., 2 (1984), pp. 130-138

Published online: 1984-02

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  • Abstract

In this note the exact non-local radiation condition and its local approximations at finite artifical boundary for the exterior boundary value problem of the reduced wave equation in 2 and 3 dimensions are discussed. Based on the asymptotic expansion of Hankel functions for large arguments, and approach for the construction of local approximations is suggested and gives expression of the normal derivative at spherial artifical boundary in terms of linear combination of Laplace-Beltrami operator and its iterates, i.e. tangential derivatives of even order exclusively. The resulting formalism is compatible with the usual variational principle and the finite element metodology and thus seems to be convenient in practical implementation.

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@Article{JCM-2-130, author = {Kang Feng}, title = {Asymptotic Radiation Conditions for Reduced Wave Equation}, journal = {Journal of Computational Mathematics}, year = {1984}, volume = {2}, number = {2}, pages = {130--138}, abstract = { In this note the exact non-local radiation condition and its local approximations at finite artifical boundary for the exterior boundary value problem of the reduced wave equation in 2 and 3 dimensions are discussed. Based on the asymptotic expansion of Hankel functions for large arguments, and approach for the construction of local approximations is suggested and gives expression of the normal derivative at spherial artifical boundary in terms of linear combination of Laplace-Beltrami operator and its iterates, i.e. tangential derivatives of even order exclusively. The resulting formalism is compatible with the usual variational principle and the finite element metodology and thus seems to be convenient in practical implementation. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9647.html} }
TY - JOUR T1 - Asymptotic Radiation Conditions for Reduced Wave Equation AU - Kang Feng JO - Journal of Computational Mathematics VL - 2 SP - 130 EP - 138 PY - 1984 DA - 1984/02 SN - 2 DO - http://dor.org/ UR - https://global-sci.org/intro/jcm/9647.html KW - AB - In this note the exact non-local radiation condition and its local approximations at finite artifical boundary for the exterior boundary value problem of the reduced wave equation in 2 and 3 dimensions are discussed. Based on the asymptotic expansion of Hankel functions for large arguments, and approach for the construction of local approximations is suggested and gives expression of the normal derivative at spherial artifical boundary in terms of linear combination of Laplace-Beltrami operator and its iterates, i.e. tangential derivatives of even order exclusively. The resulting formalism is compatible with the usual variational principle and the finite element metodology and thus seems to be convenient in practical implementation.
Kang Feng. (1970). Asymptotic Radiation Conditions for Reduced Wave Equation. Journal of Computational Mathematics. 2 (2). 130-138. doi:
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