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Article
Solving the Inverse Problems of Wave Equation by a Boundary Functional Method
Author(s)
Chein-Shan Liu and Yung-Wei Chen
Full-Text PDF XML 844 Views
DOI:10.17265/2159-5879/2017.06.002
Affiliation(s)
ABSTRACT
The inverse problems of wave equation to recover unknown space-time dependent functions of wave speed and wave source are solved in this paper, without needing of initial conditions and no internal measurement of data being required. After a homogenization technique, a sequence of spatial boundary functions at least the fourth-order polynomials are derived, which satisfy the homogeneous boundary conditions. The boundary functions and the zero element constitute a linear space, and then a new boundary functional is proved in the linear space, of which the energy is preserved for each dynamic energetic boundary function. The linear systems and iterative algorithms used to recover unknown wave speed and wave source functions with the dynamic energetic boundary functions as bases are developed, which converge fast at each time step. The input data are parsimonious, merely the measured boundary strains and the boundary values and slopes of unknown functions to be recovered. The accuracy and robustness of present methods are confirmed by comparing exact solutions with estimated results under large noises up to 20%.
KEYWORDS
Space-time dependent wave speed, space-time dependent wave source, dynamic energetic boundary functions, BFM (boundary functional method), iterative method.
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