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- Beilina, Larisa, 1970, et al.
(författare)
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Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems
- 2012
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems is the first book in which two new concepts of numerical solutions of multidimensional Coefficient Inverse Problems (CIPs) for a hyperbolic Partial Differential Equation (PDE) are presented: Approximate Global Convergence and the Adaptive Finite Element Method (adaptivity for brevity). Two central questions for CIPs are addressed: How to obtain a good approximation for the exact solution without any knowledge of a small neighborhood of this solution, and how to refine it given the approximation. The book also combines analytical convergence results with recipes for various numerical implementations of developed algorithms. The developed technique is applied to two types of blind experimental data, which are collected both in a laboratory and in the field. The result for the blind backscattering experimental data collected in the field addresses a real-world problem of imaging of shallow explosives.
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| 2. |
- Kuzhuget, A. V., et al.
(författare)
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Approximate global convergence and quasi-reversibility for a coefficient inverse problem with backscattering data
- 2012
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Ingår i: Journal of Mathematical Sciences. - : Springer Science and Business Media LLC. - 1072-3374 .- 1573-8795. ; 181:2, s. 126-163
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Tidskriftsartikel (refereegranskat)abstract
- A numerical method possessing the approximate global convergence property is developed for a 3-D coefficient inverse problem for hyperbolic partial differential equations with backscattering data resulting from a single measurement. An important part of this technique is the quasireversibility method. An approximate global convergence theorem is proved. Results of two numerical experiments are presented.
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| 8. |
- Beilina, Larisa, 1970, et al.
(författare)
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Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem
- 2010
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Ingår i: 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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Tidskriftsartikel (refereegranskat)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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