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Normal mode solutions for absorbing boundary conditions
Author(s) -
Geller Robert J.,
Noack Reinhard M.,
Fetter Alexander L.
Publication year - 1985
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/gl012i003p00145
Subject(s) - eigenvalues and eigenvectors , hermitian matrix , superposition principle , eigenfunction , boundary value problem , mathematical analysis , lanczos resampling , boundary (topology) , physics , computation , singular boundary method , robin boundary condition , mathematics , mixed boundary condition , boundary element method , quantum mechanics , finite element method , algorithm , thermodynamics
Wave propagation problems with radiation boundary conditions are non‐hermitian and therefore typically cannot be solved by expanding in terms of eigenfunctions that correspond to real eigenvalues. We present a method for solving such problems entirely in terms of a superposition of normal modes, using the "shifted eigenvalue" method outlined by Lanczos. In effect, the desired system with an outgoing radiation boundary condition is coupled to a system which is identical, but has an incoming radiation boundary condition. The combined system is hermitian, and thus has real eigenvalues. We present numerical computations for a one‐dimensional, semi‐infinite, homogeneous continuum.