Following papers are published within the Project:
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
L. Beilina and M.V. Klibanov, Relaxation property for the adaptivity for ill-posed problems, Applicable Analysis, DOI:10.1080/00036811.2013.768339, 2013.
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.
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.
Anatoly B. Bakushinsky, Alexandra B. Smirnova, and Hui Liu, Theoretical and Numerical Study of Iteratively Truncated Newton's Algorithm, Applied Inverse Problems, Springer Proceedings in Mathematics & Statistics, Vol. 48, DOI 10.1007/978-1-4614-7816-4, 2013.
L. A. Nazarova and L.A. Nazarov, Inverse Problems in Geomechanics: Diagnostics and Prediction of the State of Rock Masses with Estimating Their Properties, Applied Inverse Problems, Springer Proceedings in Mathematics & Statistics, Vol. 48, DOI 10.1007/978-1-4614-7816-4, 2013.
Aubrey Rhoden, Natee Patong, Yueming Liu, Jianzhong Su and Hanli Liu, A Globally Convergent Numerical Method for Coefficient Inverse Problems with Time-Dependent Data, Applied Inverse Problems, Springer Proceedings in Mathematics & Statistics, Vol. 48, DOI 10.1007/978-1-4614-7816-4, 2013.
A. G. Yagola, Y. M. Korolev, Error estimation in ill-posed problems in special cases,Applied Inverse Problems, Springer Proceedings in Mathematics & Statistics, Vol. 48, DOI 10.1007/978-1-4614-7816-4, 2013.
Kuramshina, I. Kochikov and A. Yagola, Stable numerical methods of approaching quantum mechanical molecular force fields to experimental data, Applied Inverse Problems, Springer Proceedings in Mathematics & Statistics, Vol. 48, DOI 10.1007/978-1-4614-7816-4, 2013.
Thouraya N. Baranger B. Tomas Johansson and Romain Rischette, On the alternating method for Cauchy problems and its finite element discretisation, Applied Inverse Problems, Springer Proceedings in Mathematics & Statistics, Vol. 48, DOI 10.1007/978-1-4614-7816-4, 2013.
V. P. Gubatenko On the formulation of inverse problem in electrical prospecting, Inverse Problems and Large-Scale Computations, Springer Proceedings in Mathematics & Statistics, Vol. 52, DOI: 10.1007/978-3-319-00660-4, 2013.
L. Angermann, V. Yatsyk et al Preset field approximation and self-consistent analysis of the scattering and generation of oscillations by a layered structure, Inverse Problems and Large-Scale Computations, Springer Proceedings in Mathematics & Statistics, Vol. 52, DOI: 10.1007/978-3-319-00660-4, 2013.
L. Angermann A posteriori estimates for errors of functionals on finite volume approximations to solutions of elliptic boundary value problems, Inverse Problems and Large-Scale Computations, Springer Proceedings in Mathematics & Statistics, Vol. 52, DOI: 10.1007/978-3-319-00660-4, 2013.
D. Valovik Electromagnetic wave propagation in nonlinear layered waveguide structures: Computational approach to determine propagation constants, Inverse Problems and Large-Scale Computations, Springer Proceedings in Mathematics & Statistics, Vol. 52, DOI: 10.1007/978-3-319-00660-4, 2013.
V. Trofimov, O. Matusevich, I. Shirokov, and M. Fedotov Performance of multi-cores and multiprocessor computers for some 3D problems of nonlinear optics and gaseous dynamics, Inverse Problems and Large-Scale Computations, Springer Proceedings in Mathematics & Statistics, Vol. 52, DOI: 10.1007/978-3-319-00660-4, 2013.
AP Smirnov et al. Modeling of electromagnetic wave propagation in guides with inhomogeneous dielectric inclusions, Inverse Problems and Large-Scale Computations, Springer Proceedings in Mathematics & Statistics, Vol. 52, DOI: 10.1007/978-3-319-00660-4, 2013.
A. Frolov and E. Kartchevskiy, Integral equation methods in optical waveguide theory, Inverse Problems and Large-Scale Computations, Springer Proceedings in Mathematics & Statistics, Vol. 52, DOI: 10.1007/978-3-319-00660-4, 2013.
Y. Podlipenko and Y Shestopalov, Guaranteed estimates of functional from solutions and data of interior Maxwell problems under uncertainties, Inverse Problems and Large-Scale Computations, Springer Proceedings in Mathematics & Statistics, Vol. 52, DOI: 10.1007/978-3-319-00660-4, 2013.
Y. Smirnov, Y. Shestopalov, and E. Derevyanchuk, Permittivity Reconstruction of Layered Dielectrics in a Rectangular Waveguide From the Transmission Coefficients at Different Frequencies, Inverse Problems and Large-Scale Computations, Springer Proceedings in Mathematics & Statistics, Vol. 52, DOI: 10.1007/978-3-319-00660-4, 2013.
A. Samokhina and E. Trahtengerts, Computer algorithms for processing large information volumes to make decision on countermeasures for multiple emergencies occurring simultaneously, Inverse Problems and Large-Scale Computations, Springer Proceedings in Mathematics & Statistics, Vol. 52, DOI: 10.1007/978-3-319-00660-4, 2013.
V. Yatsyk, System of nonlinear boundary-value problems and self-consistent analysis of resonance scattering and generation of oscillations by a cubically polarisable layered structure, Inverse Problems and Large-Scale Computations, Springer Proceedings in Mathematics & Statistics, Vol. 52, DOI: 10.1007/978-3-319-00660-4, 2013.
L. Beilina and M.V. Klibanov, 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.
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.
L. Beilina, Adaptive Finite Element Method for a coefficient inverse problem for the Maxwell's system. Applicable Analysis. 90 (10) s. 1461-1479, 2011.
Beilina, L. ; Klibanov, M. ; Kuzhuget, A. 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, 2011.
Klibanov, M. V. ; Bakushinsky, A. B. ; Beilina, L. 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, 2011.
Beilina, L. ; Klibanov, M. V. ; Kokurin, M. Y. 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, 2010.
Beilina, L. ; Klibanov, M. V. A posteriori error estimates for the adaptivity technique for the Tikhonov functional and global convergence for a coefficient inverse problem. Inverse Problems, 26, 2010.
Beilina, L. ; Klibanov, M. V. Reconstruction of dielectrics from experimental data via a hybrid globally convergent/adaptive inverse algorithm. Inverse Problems. 26, 2010.
Beilina, L. ; Grote, M. Adaptive Hybrid Finite Element/Difference method for Maxwell's equations. TWMS Journal of Pure and Applied Mathematics. 1 (2) s. 176-197, 2010.
Beilina, L. ; Klibanov, M. V. 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, 2010.
Klibanov, M. V. ; Fiddy, M. A. ; Beilina, L. et al. Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem. Inverse Problems. 26 (4), 2010.
N.A. Koshev, N.A. Orlikovsky, E.I. Rau, A.G. Yagola. Solution of the inverse problem of restoring the signals from an electronic microscope in the backscattered electron mode on the class of bounded variation functions. - Numerical Methods and Programming, 2011, v. 12, pp. 362-367 (in Russian). http://num-meth.srcc.msu.ru/english/zhurnal/tom_2011/v12r142.html
Yu.M. Korolev, A.G. Yagola. Error estimation in linear inverse problems with prior information. - Numerical Methods and Programming, 2012, v. 13, pp. 14-18 (in Russian). http://num-meth.srcc.msu.ru/english/zhurnal/tom_2012/v13r102.html
A. Bakushinskiy. A posteriori error estimates for approximate solutions of irregular operator equations. Doklady of Mathematics V.437, n.4, pp. 439--440, 2011.
G. Bocharov, I. Gainova , (together with V. Chereshnev, S. Bazhan, B Bachmetyev, J. Argilaguet, J. Martinez, A Meyerhans), Human Immunodeficiency Virus Infection: from Biological Observations to Mechanistic Mathematical Modelling, 2012.
V.G. Romanov, A two-dimensional inverse problem for the viscoelasticity equation, Siberian Mathematical Journal, Vol.53, No. 6,pp.1128-1138, 2012
V.G. Romanov, A.L. Nazarov, Uniqueness theorem in inverse problem of integral-differential equation in electrodynamics, Siberian Journal of Industrial Mathematics, V.15, 77-86 (in Russian), 2012.
Y. Shestopalov, Y. Smirnov, Determination of permittivity of an inhomogeneous dielectric body in a waveguide. Inverse Problems, 2011, Vol. 27, pp. 095010-095022.
Y. Shestopalov, Y. Smirnov. Inverse scattering in guides. Journal of Physics: Conference Series, 2012, Vol. 346. p. 012019.
Y. Smirnov, Y. Shestopalov, Numerical-analytical methods for the analysis of forward and inverse scattering by dielectric bodies in waveguides. Proc. MIKON 2012, Warsaw, Poland, May 21-23, 2012, pp. 127–132. DOI 10.1109/MIKON.2012.6233493
Y. Smirnov, Y. Shestopalov, and E. Derevyanchuk, Permittivity Determination of Multi-sectional Diaphragm with Metamaterial Layers in Rectangular Waveguide. Proc. PIERS, Taipei, Taiwan, March 25–28, 2013, pp. 135–139.
Y. Shestopalov, Y. Smirnov, Eigenwaves in waveguides with dielectric inclusions: spectrum. Applicable Analysis, 2013. DOI: 10.1080/00036811.2013.778980.
Angermann L., Shestopalov Y.V., Yatsyk V.V., Modeling and analysis of wave packet scattering and generation for a nonlinear layered structure. Proc. of the 14-th Seminar Computer Modeling in Microwave Engineering and Applications. Bayreuth, Germany, March 5-6, 2012, pp. 21-26.
Y. Podlipenko, Y, Shestopalov, Guaranteed Estimates of Functionals from Solutions and Right-hand Sides of Maxwell Equations under Uncertainties. Proc. PIERS, Moscow, 19-23 August, 2012
Y. Podlipenko, Y. Shestopalov, Guaranteed estimates of linear continuous functionals of solutions and right-hand sides of the Helmholtz equation in the domains with infinite boundaries under uncertainties. Proc. PIERS, Stockholm, Sweden, August 12-15, 2013, 5 p.
Y. Shestopalov, Some fundamental issues of the mathematical theory of wave propagation, Proc. First International Research and Practice Conf. “Topical issues and perspectives in the development of radio engineering and info-communication systems”, Moscow, MIREA, March 28-30, 2013, pp. 256-259.
Y. Shestopalov, P. Tomasek, Parameter optimization of waveguide frequency filters, Proc. First International Research and Practice Conf. “Topical issues and perspectives in the development of radio engineering and info-communication systems”, Moscow, MIREA, March 28-30, 2013, pp. 259-263
Y. Shestopalov, E. Chernokozhin, On solution to integral equations with a logarithmic singularity of the kernel on several intervals of integration: elements of the spectral theory, Visn. Kharkiv National University, no 1058, 2013, pp. 183-188.
Y. Shestopalov, Spectral Theory of Wave Propagation: Survey of Recent Results, Proc. PIERS, Stockholm, Sweden, August 12–15, 2013
Y. Shestopalov, A. Smirnov, A. Semenov, FDTD Simulation of Waveguide with Non-uniform Dielectric Slab, Proc. PIERS, Stockholm, Sweden, August 12–15, 2013
Y. Shestopalov, P. Tomasek, Parameter Optimization of Waveguide Filters Employing Analysis of Closed-form Solution, Proc. PIERS, Stockholm, Sweden, August 12–15, 2013
Y. Shestopalov, E. Karchervskiy, Mathematical and Numerical Analysis of Dielectric Waveguides by the Integral Equation Method, Proc. PIERS, Stockholm, Sweden, August 12–15, 2013
A. Samokhin, Y. Shestopalov, K. Kobayashi, Stationary Iteration Methods for Solving 3D Electromagnetic Scattering Problems, Appl. Maths. Comp., 2013
Publications with direct links:
G. Bocharov, I. Gainova , (together with V. Chereshnev, S. Bazhan, B Bachmetyev, J. Argilaguet, J. Martinez, A Meyerhans), Human Immunodeficiency Virus Infection: from Biological Observations to Mechanistic Mathematical Modelling, 2012.
V.G. Romanov, A two-dimensional inverse problem for the viscoelasticity equation, Siberian Mathematical Journal, Vol.53, No. 6,pp.1128-1138, 2012.
V.G. Romanov, A.L. Nozarov, Uniqueness theorem in inverse problem of integral-differential equation in electrodynamics, Siberian Journal of Industrial Mathematica, V15.,77-86 (in russian)
L.Beilina, Adaptive Finite Element Method for a coefficient inverse problem for the Maxwell's system, Applicable Analysis, iFirst, 1-19, 2011.Paper is available to download at Chalmers Publication Library.
L.Beilina, Adaptive Hybrid Finite Element/Difference Method for Maxwell's Equations: an a Priori Error Estimate and Efficiency, Applied and Computational Mathematics (ACM), V.9(2), 2010. Paper is available to download at Chalmers Publication Library.
M.Asadzadeh and L.Beilina, A posteriori error analysis in a globally convergent numerical method for a hyperbolic coefficient inverse problem, Inverse Problems, 26, 115007, 2010.Paper is available to download at Chalmers Publication Library.
L.Beilina, M. Grote, Adaptive Hybrid Finite Element/Difference Method for Maxwell's equations,TWMS J. of Pure and Applied Mathematics, V.1(2), pp. 196-197, 2010 Paper is available to download at Chalmers Publication Library.
A.Kuzhuget, L.Beilina, M.V.Klibanov, V.G.Romanov, Global convergence and quasi-reversibility for a coefficient inverse problem with backscattered data, submitted to SIAM J.Numerical Analysis, 2010. Paper is available to download at Chalmers Publication Library.
L.Beilina, M.V.Klibanov, A.Kuzhuget, 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, 449-476, 2011. Paper is available to download at Chalmers Publication Library.
L.Beilina, M.V.Klibanov, Reconstruction of dielectrics from experimental data via a hybrid globally convergent/adaptive inverse algorithm, Inverse Problems, 26, 125009, 2010. Paper is available to download at Chalmers Publication Library.
M.V.Klibanov, A.B.Bakushinsky, L.Beilina, Why a minimizer of the Tikhonov functional is closer to the exact solution than the first guess, J. Inverse and Ill-posed problems, 2010. Paper is available to download at Chalmers Publication Library.
A.B. Bakushinksy, A Posteriori Error Estimates for Approximate Solutions of Irregular Operator Equations.