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  • 1.
    Podlipenko, Y.
    et al.
    Kiev University, Kiev, Ukraine.
    Shestopalov, Yury V.
    arlstad University, Karlstad, Sweden.
    Guaranteed Estimates of Functionals from Solutions and Data of Interior Maxwell Problems Under Uncertainties2013In: Springer Proceedings in Mathematics & statistics, ISSN 2194-1017, E-ISSN 2194-1009, Vol. 52, p. 135-167Article in journal (Refereed)
    Abstract [en]

    We are looking for linear with respect to observations optimal estimates of solutions and right-hand sides of Maxwell equations called minimax or guaranteed estimates. We develop constructive methods for finding these estimates and estimation errors which are expressed in terms of solutions to special variational equations and prove that Galerkin approximations of the obtained variational equations converge to their exact solutions.

  • 2.
    Smirnov, A.
    et al.
    Lomonosov Moscow State University, Moscow, Russian Federation.
    Semenov, A.
    Lomonosov Moscow State University, Moscow, Russian Federation.
    Shestopalov, Yury V.
    Karlstad University, Karlstad, Sweden.
    Modeling of Electromagnetic Wave Propagation in Guides with Inhomogeneous Dielectric Inclusions2013In: Springer Proceedings in Mathematics & statistics, ISSN 2194-1017, E-ISSN 2194-1009, Vol. 52, p. 113-118Article in journal (Refereed)
    Abstract [en]

    We consider scattering in the time domain of electromagnetic waves from inhomogeneous dielectric inclusions in a 3D waveguide of rectangular cross section. All electromagnetic field components are calculated, and transport of energy in the guide is investigated using finite difference time domain (FDTD) method in different frequency ranges. An efficient 3D FDTD EMWSolver3D solver for the nonstationary Maxwell equation system is used. The model computations are performed for the H10-mode scattering from parallelepiped-shaped dielectric inclusions. Attenuation and propagation factors are calculated for the transmitted modes and field distributions are visualized. The present method can be used for a wide class of waveguide problems that meet substantial difficulties as far as numerical solution by conventional FDTD methods is concerned due to complex geometries or computational requirements. The solver employs algorithms of parallel computations and is implemented on supercomputers of last generation for solving large-scale problems with characteristic matrix dimensions achieving 1012.

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