Simultaneous reconstruction of material and transient source parameters using the invariant imbedding method
In: Journal of Mathematical Physics, Jg. 34 (1993-05-01), S. 1824-1845
Online
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Zugriff:
This paper extends the time domain wave splitting and invariant imbedding method to an inhomogeneous wave equation with a source term: uxx−utt+A(x)ux=2D(x)i’(t). The direct scattering and inverse source problems of this equation are studied. Operators J± that map the source function into the scattered waves at the edges of the slab are defined. A system of coupled nonlinear integrodifferential equations for these scattering operator kernels is obtained. The direct scattering problem is to obtain the scattering operator kernels J± and R+ when parameters A and D are given. The inverse problem is to simultaneously reconstruct A(x) and D(x) from the scattering operator kernels R+(0,t), 0≤t≤2 and J−(0,t), 0≤t≤1. Both numerical inversion algorithms and the small time approximate reconstruction method are presented. A Green’s function technique is used to derive Green’s operator kernel equations for the calculation of the internal field. It provides an alternative effective and fast way to compute the scatterin...
Titel: |
Simultaneous reconstruction of material and transient source parameters using the invariant imbedding method
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Autor/in / Beteiligte Person: | Sun, Zhiming ; Corones, James |
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Zeitschrift: | Journal of Mathematical Physics, Jg. 34 (1993-05-01), S. 1824-1845 |
Veröffentlichung: | AIP Publishing, 1993 |
Medientyp: | unknown |
ISSN: | 1089-7658 (print) ; 0022-2488 (print) |
DOI: | 10.1063/1.530140 |
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