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- Beilina, Larisa, 1970, et al.
(author)
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Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem
- 2010
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In: Journal of Mathematical Sciences, JMS, Springer. - : Springer Science and Business Media LLC. - 1072-3374 .- 1573-8795. ; 167:3, s. 279-325
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Journal article (peer-reviewed)abstract
- A new framework of the functional analysis is developed for the finite element adaptive method (adaptivity) for the Tikhonov regularization functional for some ill-posed problems. As a result, the relaxation property for adaptive mesh refinements is established. An application to a multidimensional coefficient inverse problem for a hyperbolic equation is discussed. This problem arises in the inverse scattering of acoustic and electromagnetic waves. First, a globally convergent numerical method provides a good approximation for the correct solution of this problem. Next, this approximation is enhanced via the subsequent application of the adaptivity. Analytical results are verified computationally. Bibliography: 30 titles. Illustration: 2 figures.
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| 5. |
- Xin, J., et al.
(author)
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Globally convergent numerical methods for coefficient inverse problems for imaging inhomogeneities
- 2010
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In: Computing in Science and Engineering, (CISE). - 1521-9615. ; 12:5, s. 64-77
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Journal article (peer-reviewed)abstract
- How can we differentiate between an underground stone and a land mine? We discuss a class of methods for solving such problems. This class of methods concerns globally convergent numerical methods for Coefficient Inverse Problems, unlike conventional locally convergent algorithms. Numerical results are presented modeling imaging of the spatially distributed dielectric permittivity function in an environment where antipersonnel land mines are embedded along with stones. While these results are concerned with the first generation of globally convergent algorithms, images obtained by the most recent second generation are also presented for a generic case of imaging of the dielectric permittivity function. The mathematical apparatus is sketched only very briefly with references to corresponding publications.
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