Publications

2016
  • L. Beilina and S. Hosseinzadegan, An adaptive finite element method in reconstruction of coefficients in Maxwell’s equations from limited observations, Applications of Mathematics, Springer, 61(3), 253-286, 2016. doi:­10.1007/s10492-016-0131-0, arxiv
  • L. Beilina, Domain decomposition finite element/finite difference method for the conductivity reconstruction in a hyperbolic equation, Communications in Nonlinear Science and Numerical Simulation, Elsevier, 2016. doi:10.1016/j.cnsns.2016.01.016, arxiv
  • E. M. Karchevskii, L. Beilina, A. O. Spiridonov and  A. I. Repina,  Reconstruction of dielectric constants of multi-layered optical fibers using propagation constants measurements, Applied and Computational Mathematics (ACMIJ), 15(3), 346-358, 2016. arxiv
  • L. Beilina, Application of the finite element method in a  quantitative imaging technique, J. Comput. Methods   Sci. Eng., IOS Press, 16(4), 755-771, 2016. doi:10.3233/JCM-160689, arxiv
  • L. Beilina, L. Mpinganzima, P. Tassin, Adaptive optimization algorithm for the computational design of nanophotonic structures. ICEAA, 2016. doi:10.1109/ICEAA.2016.7731416.
  • J. B. Malmberg, L. Beilina. Adaptive finite element  method for the solution of electromagnetic inverse problem using  limited observations, IEEE,  Proceedings of the 2016 International Conference on Electromagnetics  in Advanced Applications, ICEAA 2016. doi:10.1109/ICEAA.2016.7731417.
2015
  • L. Beilina, M. Cristofol and K. Niinimaki, Optimization  approach for the simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions from limited  observations, Inverse Problems and Imaging, 9 (1), pp.1-25, 2015. arxiv
  • L. Beilina, N. T. Thanh, M.V. Klibanov and J. B. Malmberg, Globally convergent and adaptive finite element methods in imaging of buried objects from experimental backscattering radar measurements, Journal of Computational and Applied Mathematics, Elsevier, DOI:  10.1016/j.cam.2014.11.055, 2015. arxiv
  • L. Beilina, M.V. Klibanov, Globally strongly convex cost  functional for a coefficient inverse problem,  Nonlinear analysis: real world applications, 22, 272-288, 2015. arxiv
  • N. T.  Thanh, L. Beilina, M. V. Klibanov, M. A. Fiddy, Imaging of Buried  Objects from Experimental Backscattering Time-Dependent Measurements using a Globally Convergent Inverse Algorithm,  SIAM Journal on Imaging Sciences, 8(1), 757-786, 2015. arxiv
  • L.Beilina, N. T. Thanh, M.V. Klibanov, and J. B. Malmberg, Methods of quantitative reconstruction of shapes and  refractive indices from experimental data,  Inverse Problems and Applications, Springer Proceedings in Mathematics & Statistics, Vol. 120, 2015.
  • E. Karchevskii, A. Spiridonov, and L. Beilina, Determination of permittivity from  propagation constant  measurements in optical fibers,  Inverse Problems and Applications, Springer Proceedings in Mathematics & Statistics, Vol. 120, 2015.
  • L. Beilina and A. Eriksson, Reconstruction of  dielectric constants  in a cylindrical waveguide, Inverse Problems and Applications, Springer Proceedings in Mathematics & Statistics, Vol. 120, 2015.
  • L. Beilina and  I. Gainova, Time-adaptive FEM  for distributed parameter identification in mathematical model of HIV infection with drug therapy,  Inverse Problems and Applications, Springer Proceedings in Mathematics & Statistics, Vol. 120, 2015.
  • L. Beilina  and E. Karchevskii, The layer-stripping algorithm for reconstruction of  dielectrics in an optical fiber,  Inverse Problems and Applications, Springer Proceedings in Mathematics & Statistics, Vol. 120, 2015.
  • L. Beilina, M. Cristofol and K. Niinimaki,  Simultaneous  reconstruction of Maxwell’s coefficients from   backscattering data,  Inverse Problems and Applications, Springer Proceedings in Mathematics & Statistics, Vol. 120, 2015.
2014
  • L. Beilina, Nguyen Trung Thanh, M. V. Klibanov and M. A. Fiddy,  Reconstruction from blind experimental data for an inverse problem for a hyperbolic equation,  Inverse Problems,   30, 025002,  DOI:10.1088/0266-5611/30/2/025002, 2014.arxiv
  • Nguyen Trung Thanh, L. Beilina, M. V. Klibanov and M. A. Fiddy, Reconstruction of the refractive index from experimental backscattering data using a globally convergent inverse method,  SIAM J. Scientific Computing, 36 (3), pp.273-293, 2014.arxiv
  • E. M. Karchevskii, A. L. Beilina O. Spiridonov, A.  AND I. Repina ,  Reconstruction of Dielectric Constants of Core and Cladding of Optical Fibers Using Propagation Constants Measurements,  Physics Research International, ID 253435,  2014.  DOI:10.1155/2014/253435, arxiv
  • L. Beilina, Nguyen Trung Thanh, M. V. Klibanov and J. B. Malmberg, Reconstruction of shapes and refractive indices from backscattering experimenta arxivl data using the adaptivity,  Inverse Problems, 30, 105007, 2014 arxiv
  • L. Beilina, M. V. Klibanov,  Globally strongly convex cost functional for a coefficient inverse problem,  Nonlinear analysis: real world applications, 22, 272-288, 2015 arxiv
  • L. Beilina, Nguyen Trung Thanh, M.V. Klibanov and J. B. Malmberg, Globally convergent and adaptive finite element methods in imaging of buried objects from experimental backscattering radar measurements, Journal of Computational and Applied Mathematics, Elsevier, DOI:  10.1016/j.cam.2014.11.055, 2014.arxiv
2013
  • L. Beilina, Energy estimates and numerical verification of the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system, Cent. Eur. J. Math., 2013, 11(4), 702-733
    DOI: 10.2478/s11533-013-0202-3 arxiv 
  • L. Beilina and M. V. Klibanov,  Relaxation property for the  adaptivity for ill-posed problems,  Applicable Analysis,   DOI:10.1080/00036811.2013.768339, 2013. arxiv
  • N. Koshev and L. Beilina,  An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data,  in the Topical Issue ”Numerical Methods for Large Scale Scientific Computing” of CEJM, 11(8), 1489-1509,  2013.
  • L. Beilina and M. V. Klibanov,  Approximate global convergence in imaging of land mines from backscattered data,  Applied Inverse Problems, Springer Proceedings in Mathematics & Statistics, Vol. 48,   pp. 15-35, DOI 10.1007/978-1-4614-7816-4, 2013.
  • L. Beilina and I.Gainova, Time-adaptive FEM  for distributed parameter identification in biological models,  Applied Inverse Problems, Springer Proceedings in Mathematics & Statistics, Vol. 48, pp. 37-50, DOI 10.1007/978-1-4614-7816-4, 2013.
  •  L. Beilina, M. P. Hatlo Andresen, H. E. Krogstad, Adaptive finite element method in reconstruction of dielectrics from backscattered data,  Applied Inverse Problems, Springer Proceedings in Mathematics & Statistics, Vol. 48, pp. 51-73,  DOI 10.1007/978-1-4614-7816-4,  2013.arxiv
  • N. Koshev and L. Beilina,  A posteriori error estimates for  Fredholm integral equations of the first kind,  Applied Inverse Problems, Springer Proceedings in Mathematics & Statistics, Vol. 48, pp. 75-93, DOI 10.1007/978-1-4614-7816-4,  2013.
  •  L. Beilina and M. V. Klibanov, Adaptive FEM with relaxation for a   hyperbolic coefficient inverse problem,  Applied Inverse Problems, Springer Proceedings in Mathematics & Statistics, Vol. 48, pp. 129-153, DOI 10.1007/978-1-4614-7816-4, 2013.
  • M. Asadzadeh and L. Beilina,   Adaptive approximate globally convergent algorithm with backscattered   data,  Inverse Problems and Large-Scale Computations, Springer Proceedings in Mathematics & Statistics, Vol. 52, pp.1-20, DOI: 10.1007/978-3-319-00660-4, 2013.
  •  J. Bondestam Malmberg and L. Beilina, Approximate globally convergent algorithm with applications in electrical prospecting,  Inverse Problems and Large-Scale Computations, Springer Proceedings in Mathematics & Statistics, Vol. 52, pp. 29-40, DOI: 10.1007/978-3-319-00660-4, 2013.
2012
  • L. Beilina and M.V. Klibanov,   a,  A new approximate mathematical model for global convergence for a coefficient inverse problem with back­scattering data. J. Inverse and Ill-Posed Problems, 20, 513-565, 2012. doi:10.1515/jip-2012-0063, arxiv
  • A.V. Kuzhuget, L. Beilina, M.V. Klibanov, A. Sullivan, L. Nguyen and M.A . Fiddy, Blind backscattering experimental data collected in the field and an approximately globally convergent inverse algorithm, Inverse Problems, 28, 095007, 2012.
  • A.V. Kuzhuget, L. Beilina, M.V. Klibanov, A. Sullivan, L. Nguyen and M.A. Fiddy, Quantitative image recovery from measured blind backscattered data using a globally convergent inverse method, IEEE Transactions of Geoscience and Remote Sensing, doi:10.1109/TGRS.2012.2211885, 2012.
  • L. Beilina and M.V. Klibanov, The philosophy of the approximate global convergence for multidimensional coefficient inverse problems, Complex Variables and Elliptic Equations, 57, 277-299, 2012.
  • A.V. Kuzhuget, L. Beilina and M.V. Klibanov, Approximate global convergence and quasi-reversibility for a coefficient inverse problem with backscattering data, J. of Mathematical Sciences, 181, 126-163, 2012.
2011
  • Beilina, L. (2011). Adaptive Finite Element Method for a coefficient inverse problem for the Maxwell’s system. Applicable Analysis. 90 (10) s. 1461-1479. Nr. 150916
  • Beilina, L. (2011). Domain decomposition finite element/finite difference approach for the Maxwell’s system in time domain.Nr. 142368
  • Beilina, L. ; Hatlo Andresen, M. P. ; Krogstad, H. E. (2011). Reconstruction of dielectrics in a symmetric structure via adaptive algorithm with backscattering data. Nr. 147043
  • Beilina, L. ; Klibanov, M. ; Kuzhuget, A. (2011). New a posteriori error estimates for adaptivity technique and global convergence for a hyperbolic coefficient inverse problem. Journal of Mathematical Sciences, JMS, Springer. 172 (4) s. 449-476. Nr. 150905
  • Beilina, L. ; Klibanov, M. (2011). The philosophy of the approximate global convergence for multidimensional coefficient inverse problems. Complex variables and elliptic equations. s. 1-23. Nr. 149534
  • Klibanov, M. V. ; Bakushinsky, A. B. ; Beilina, L. (2011). Why a minimizer of the Tikhonov functional is closer to the exact solution than the first guess. Journal of Inverse and Ill – Posed Problems. 19 (1) s. 83-105. Nr. 140758
  • Koshev, N. ; Beilina, L. (2011). Adaptive finite element method for the Fredholm integral equation of the first kind and its verification on the experimental data. Nr. 150422
  • Kuzhuget, A. V. ; Beilina, L. ; Klibanov, M. V. et al. (2011). Blind backscattering experimental data collected in the field and an approximately globally convergent inverse algorithm. Nr. 148369
  • Kuzhuget, A. V. ; Beilina, L. ; Klibanov, M. V. et al. (2011). Approximate global convergence and quasi-reversibility for a coefficient inverse problem with backscattering data. Nr. 139881
2010
  • Asadzadeh, M. ; Beilina, L. (2010). A posteriori error estimates in a globally convergent FEM for a hyperbolic coefficient inverse problem. Inverse Problems. 26 (11) Nr. 128783
  • Asadzadeh, M. ; Beilina, L. (2010). A posteriori error estimates in a globally convergent FEM for a hyperbolic coefficient inverse problem. Nr. 136403
  • Beilina, L. (2010). Adaptive Hybrid Finite Element/Difference method for Maxwell’s equations: an a priory error estimate and efficiency. Applied and Computational Mathematics (ACM). 9 (2) s. 176-197. Nr. 131091
  • Beilina, L. ; Suschenko, A. (2010). Recent Advances in Numerical Methods for Inverse Problems Resolution. AIP Conference Proceedings; International Conference on Numerical Analysis and Applied Mathematics Rhodes, GREECE, SEP 19-25, 2010. 1281 s. 1051. ISBN/ISSN: 978-0-7354-0834-0 Nr. 139661
  • Beilina, L. (2010). Adaptive finite element method for a coefficient inverse problem for the Maxwell’s system. Nr. 121892
  • Beilina, L. ; Klibanov, M. V. ; Kokurin, M. Y. (2010). Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem. Journal of Mathematical Sciences, JMS, Springer. 167 (3) s. 279-325. Nr. 131090
  • Beilina, L. ; Klibanov, M. V. (2010). A posteriori error estimates for the adaptivity technique for the Tikhonov functional and global convergence for a coefficient inverse problem. Inverse Problems. 26 (4) s. (Article Number: 045012). Nr. 122621
  • Beilina, L. ; Klibanov, M. V. (2010). Reconstruction of dielectrics from experimental data via a hybrid globally convergent/adaptive inverse algorithm. Nr. 125906
  • Beilina, L. (2010). Adaptive Finite Element Method for an Electromagnetic Coefficient Inverse Problem. AIP Conference Proceedings; International Conference on Numerical Analysis and Applied Mathematics Rhodes, GREECE, SEP 19-25, 2010. 1281 s. 1052-1055 . ISBN/ISSN: 978-0-7354-0834-0 Nr. 139665
  • Beilina, L. (2010). Hybrid Discontinuous Finite Element/Finite Difference Method for Maxwell’s Equations. AIP Conference Proceedings; International Conference on Numerical Analysis and Applied Mathematics Rhodes, GREECE, SEP 19-25, 2010. 1281 s. 324-328. ISBN/ISSN: 978-0-7354-0834-0 Nr. 139660
  • Beilina, L. ; Klibanov, M. V. (2010). Reconstruction of dielectrics from experimental data via a hybrid globally convergent/adaptive inverse algorithm. Inverse Problems. 26 s. 125009 (30 pages). Nr. 131094
  • Beilina, L. ; Grote, M. (2010). Adaptive Hybrid Finite Element/Difference method for Maxwell’s equations. TWMS Journal of Pure and Applied Mathematics. 1 (2) s. 176-197. Nr. 131092
  • Beilina, L. ; Klibanov, M. V. (2010). Synthesis of global convergence and adaptivity for a hyperbolic coefficient inverse problem in 3D. Journal of Inverse and Ill-Posed Problems. 18 (1) s. 85-132. Nr. 122453
  • Beilina, L. ; Klibanov, M. V. (2010). Global convergence for Inverse Problems. AIP Conference Proceedings; International Conference on Numerical Analysis and Applied Mathematics Rhodes, GREECE, SEP 19-25, 2010. 1281 s. 1056-1058 . ISBN/ISSN: 978-0-7354-0834-0 Nr. 139669
  • Klibanov, M. V. ; Fiddy, M. A. ; Beilina, L. et al. (2010). Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem. Inverse Problems. 26 (4) s. (Article Number: 045003). Nr. 122620
  • Klibanov, M. V. ; Fiddy, M. A. ; Beilina, L. et al. (2010). Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem. Nr. 110992
  • Xin, J. ; Beilina, L. ; Klibanov, M. V. (2010). Globally convergent numerical methods for coefficient inverse problems for imaging inhomogeneities. Computing in Science and Engineering, (CISE). 12 (5) s. 64-77. Nr. 131088

2009

  • Beilina, L. ; Klibanov, M. V. (2009). A globally convergent numerical method and the adaptivity technique for a hyperbolic coefficient inverse problem. Part I: analytical study. Nr. 96280
  • Beilina, L. ; Hatlo, M. P. ; Krogstad, H. E. (2009). Adaptive algorithm for an inverse electromagnetic scattering problem.Applicable Analysis. 88 (1) s. 15-28. Nr. 104799
  • Beilina, L. ; Klibanov, M. V. (2009). A Globally Convergent Numerical Method and Adaptivity for a Hyperbolic Coefficient Inverse Problem. Nr. 94767
  • Beilina, L. ; Klibanov, M. V. ; Kokurin, M. Y. (2009). Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem. Nr. 102072
  • Beilina, L. ; Klibanov, M. V. (2009). A globally convergent numerical method and the adaptivity technique for a hyperbolic coefficient inverse problem. Part II: numerical studies. Nr. 96282
  • Beilina, L. ; Klibanov, M. V. (2009). Synthesis of Global Convergence and Adaptivity for a Hyperbolic Coefficient Inverse Problems in 3D. Nr. 94772
  • Beilina, L. ; Klibanov, M. V. (2009). A posteriori error estimates for the adaptivity technique for the Tikhonov functional and global convergence for a coefficient inverse problem. Nr. 106782
  • Xin, J. ; Beilina, L. ; Klibanov, M. V. (2009). Globally convergent numerical methods for coefficient inverse problems for imaging inhomogeneities. Nr. 96283

2008

  • Beilina, L. ; Klibanov, M. V. (2008). A globally convergent numerical method for a coefficient inverse problem. SIAM J.Sci.Comp.. 31 (1) s. 478-509. Nr. 104584

2006

  • Beilina, L. ; Clason, C. (2006). An adaptive hybrid FEM/FDM method for an inverse scattering problem in scanning acoustic microscopy. SIAM J.Sci.Comp.. 28 (1) s. 382-402. Nr. 104578

2005

  • Beilina, L. ; Johnson, C. (2005). A posteriori error estimation in computational inverse scattering. Mathematical Models in Applied Sciences. 15 (1) s. 23-35. Nr. 104593

2003

  • Beilina, L. (2003). Adaptive finite element/difference methods for time-dependent inverse scattering problems. Göteborg: Chalmers University of Technology. Doctoral thesisNr. 179
  • Beilina, L. (2003). Adaptive hybrid finite element/difference methods: applications to inverse elastic scattering. J.Inverse and Ill-posed problems. 11 (6) s. 585-618. Nr. 104582

2002

  • Beilina, L. (2002). Adaptive hybrid FEM/FDM methods for inverse scattering problems. Nr. 93866
  • Beilina, L. (2002). Adaptive hybrid FEM/FDM methods for inverse scattering problems. Inverse problems and information technologies. 1 (3) s. 73-116. Nr. 104801
  • Beilina, L. (2002). Adaptive Finite element/Difference methods for inverse elastic scattering waves. Applied Computational Mathematics. 1 (2) s. 158-174. Nr. 104800

1999

  • Beilina, L. (1999). Osmotic mass transfer through a cylindric semipermeable membrane. Nr. 92711