References
- Beilina L, Klibanov MV, Kokurin M. Yu. Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem. Journal of Mathematical Sciences. 2010;167:279–325.
- Asadzadeh M, Beilina L. A posteriori error analysis in a globally convergent numerical method for a hyperbolic coefficient inverse problem. Inverse Problems. 2010;26:115007.
- Beilina L, Johnson C. A hybrid FEM/FDM method for an inverse scattering problem. In Numerical Mathematics and Advanced Applications - ENUMATH 2001, Springer-Verlag, Berlin, 2001.
- Beilina L. Adaptive finite element/difference method for inverse elastic scattering waves. Applied and Computational Mathematics. 2002;1:158–174.
- Beilina L, Johnson C. A posteriori error estimation in computational inverse scattering. Mathematical Models and Methods in Applied Sciences. 2005;15:23–37.
- Beilina L, Clason C. An adaptive hybrid FEM/FDM method for an inverse scattering problem in scanning acoustic microscopy. SIAM Journal on Scientific Computing. 2006;28:382–402.
- Beilina L. Adaptive finite element method for a coefficient inverse problem for the Maxwell’s system. Applicable Analysis. 2011;90:1461–1479.
- Beilina L, Klibanov MV. Synthesis of global convergence and adaptivity for a hyperbolic coefficient inverse problem in 3D. Journal of Inverse and III-posed Problems. 2010;18:85–132.
- Beilina L, Klibanov MV. A posteriori error estimates for the adaptivity technique for the Tikhonov functional and global convergence for a coefficient inverse problem. Inverse Problems. 2010;26:045012.
- Beilina L, Klibanov MV. Reconstruction of dielectrics from experimental data via a hybrid globally convergent/adaptive inverse algorithm. Inverse Problems. 2010;26:125009.
- Beilina L, Klibanov MV. Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems. New York (NY): Springer; 2012.
- Klibanov MV, Bakushinskii AB. Why a minimizer of the Tikhonov functional is closer to the exact solution than the first guess. Journal of Inverse and III-posed Problems. 2011;19:83–105.
- Bakushinskii AB, Kokurin MYu. Iterative Methods for Approximate Solution of Inverse Problems. New York (NY): Springer; 2004.
- Kabanikhin SI. Inverse and Ill-posed problems. De Gruyter, Berlin: Theory and Applications; 2012.
- Tikhonov AN, Arsenin VY. Solutions of Ill-posed problems. Washington (DC): Winston and Sons; 1977.
- Tikhonov AN, Goncharsky AV, Stepanov VV, Yagola AG. Numerical methods for the solution of Ill-posed problems. London: Kluwer; 1995.
- Tikhonov AN, Leonov AS, Yagola AG. Nonlinear Ill-posed problems, V. 1, V. 2. London: Chapman and Hall; 1998.
- Engl HW, Hanke M, Neubauer A. Regularization of inverse problems. Boston: Kluwer Academic; 2000.
- Becker R, Rannacher R. An optimal control approach to a posteriori error estimation in finite element method. Acta Numerica. 2001;10:1–102.
- Beilina L, Klibanov MV. A globally convergent numerical method for a coefficient inverse problem. SIAM Journal on Scientific Computing. 2008;31:478–509.
- Beilina L, Klibanov MV. A new approximate mathematical model for global convergence for a coefficient inverse problem with backscattering data. Journal of Inverse and III-posed Problems. 2012;20:513–565.
- Klibanov MV, Fiddy MA, Beilina L, Pantong N, Schenk J. Picosecond scale experimental verification of a globally convergent numerical method for a coefficient inverse problem. Inverse Problems. 2010;26:045003.
- Klibanov MV. Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems. Journal of Inverse and III-posed Problems. arXiv: 1210.1780v1 [math-ph].
- Kuzhuget AV, Beilina L, Klibanov MV. Approximate global convergence and quasi-reversibility for a coefficient inverse problem with backscattered data. Journal of Mathematical Sciences. 2012;181:19–49.
- Kuzhuget AV, Beilina L, Klibanov MV, Sullivan A, Nguyen L, Fiddy MA. Blind experimental data collected in the field and an approximately globally convergent inverse algorithm. Inverse Problems. 2012;28:095007.
- Bangerth W, Joshi A. Adaptive finite element methods for the solution of inverse problems in optical tomography. Inverse Problems. 2008;24:034011.
- Koshev N, Beilina L. An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data. Central European Journal of Mathematics. in press.
- Feng T, Yan N, Liu W. Adaptive finite element methods for the identification of distributed parameters in elliptic equation. Advances in Computational Mathematics. 2008;29:27–53.
- Li J, Xie J, Zou J. An adaptive finite element reconstruction of distributed fluxes. Inverse Problems. 2011;27:075009.
- Ammari H, Garnier J, Kang H, Lim M, Solna K. Multistatic imaging of extended targets. SIAM Journal on Imaging Sciences. 2012;5:564–600.
- Ammari H, Kang H, Lim M, Zribi H. The generalized polarization tensors for resolved imaging. Part I: Shape reconstruction of a conductivity inclusion. Mathematics of Computation. 2012;81:367–386.
- Ammari H, Kang H, Kim E, Lee J-Y. The generalized polarization tensors for resolved imaging. Part II: Shape and electromagnetic parameters reconstruction of an electromagnetic inclusion from multistatic measurements. Mathematics of Computation. 2012;81:839–860.
- Ammari H, Boulier T, Garnier J, Jing W, Kang H, Wang H. Target identification using dictionary matching of generalized polarization tensors. 2012;arXiv:1204.3035.
- Ramlau R. TIGRA - an iterative algorithm for regularizing nonlinear ill-posed problems. Inverse Problems. 2003;19:433–465.
- Eriksson K, Estep D, Johnson C. Calculus in several dimensions. Berlin: Springer; 2004.
- Colton D, Kress R. Inverse acoustic and electromagnetic scattering theory. New York (NY): Springer; 1992.
- Reitz JR, Milford FJ, Christy RW. Foundations of electromagnetic theory. Reading (MA): Addison-Wesley; 1980.
- Beilina L. Energy estimates and numerical verification of the stabilized domain decomposition finite element/finite difference approach for the Maxwell’s system in time domain. Central European Journal of Mathematics, accepted for publication in 2012; preprint is available online at http://publications.lib.chalmers.se/publication/142368
- Bukhgeim AL, Klibanov MV. Uniqueness in the large of a class of multidimensional inverse problems. Soviet Mathematics Doklady. 1981;17:244–247.
- Bukhgeim AL. Carleman estimates for Volterra operators and uniqueness of inverse problems. In Non-Classical Problems of Mathematical Physics. Published by Computing Center of the Siberian Branch of Russian Academy of Science, Novosibirsk; 1981; p. 54–64 (in Russian).
- Klibanov MV. Uniqueness of solutions in the ‘large’ of some multidimensional inverse problems. In Non-Classical Problems of Mathematical Physics. Published by Computing Center of the Siberian Branch of the Russian Academy of Science, Novosibirsk; 1981; p. 101–114 (in Russian).
- Bukhgeim AL. Introduction in the theory of inverse problems. Utrecht: VSP; 2000.
- Klibanov MV. Inverse problems in the ‘large’ and Carleman bounds. Differential Equations. 1984;20:755–760.
- Klibanov MV. Inverse problems and Carleman estimates. Inverse Problems. 1992;8:575–596.
- Klibanov MV, Timonov A. Carleman estimates for coefficient inverse problems and numerical applications. Utrecht: VSP; 2004.
- Klibanov MV. Uniqueness of an inverse problem with single measurement data generated by a plane wave in partial finite differences. Inverse Problems. 2011;27:115005.
- Yamamoto M. Carleman estimates for parabolic equations and applications. Inverse Problems. 2009;25:123013.
- Nocedal J. Updating quasi-Newton matrices with limited storage. Mathematics of Computation. 1991;35:773–782.
- Beilina L, Samuelsson K, Åhlander K. Efficiency of a hybrid method for the wave equation. In International Conference on Finite Element Methods: Gakuto International Series Mathematical Sciences and Applications. Gakkotosho CO., LTD.; 2001.
- The software package WavES. Available from: http://waves24.com
- Engquist B, Majda A. Absorbing boundary conditions for the numerical simulation of waves. Mathematics of Computation. 1977;31:629–651.