| 1. |
- Beilina, Larisa, 1970, et al.
(författare)
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Methods of quantitative reconstruction of shapes and refractive indices from experimental data
- 2015
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Ingår i: Inverse Problems and Applications; (papers from: 3rd Annual Workshop on Inverse Problems, 2013; Stockholm; Sweden; 2 - 6 May 2013); (Proceedings in Mathematics & Statistics). - Cham : Springer International Publishing. - 2194-1009 .- 2194-1017. - 9783319124988 ; 120, s. 13-41
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Konferensbidrag (refereegranskat)abstract
- In this chapter we summarize results of [5, 6, 14] and present new results of reconstruction of refractive indices and shapes of objects placed in the air from blind backscattered experimental data using two-stage numerical procedure of [4]. Data are collected using a microwave scattering facility which was built at the University of North Carolina at Charlotte. On the first stage the approximately globally convergent method of [4] is applied to get a good first approximation for the exact solution. Results of this stage are presented in [5, 14]. On the second stage the local adaptive finite element method of [1] is applied to refine the solution obtained on the first stage. In this chapter we briefly describe methods and present new results for both stages.
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| 2. |
- Beilina, Larisa, 1970, et al.
(författare)
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Reconstruction of dielectric constants in a cylindrical waveguide
- 2015
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Ingår i: Springer Proceedings in Mathematics and Statistics:3rd Annual Workshop on Inverse Problems, 2013, Stockholm, Sweden, 2-6 May 2013. - Cham : Springer International Publishing. - 2194-1009 .- 2194-1017. - 9783319124988 ; 120, s. 97-109
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Konferensbidrag (refereegranskat)abstract
- We present the model of reconstruction of two constant complex dielectrics in a cylindrical waveguide using frequency domain measurements at the one point of a waveguide. We formulate two gradient-like methods to reconstruct these coefficients and present numerical examples showing performance of reconstruction.
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| 3. |
- Beilina, Larisa, 1970, et al.
(författare)
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Simultaneous reconstruction of Maxwell’s coefficients from backscattering data
- 2015
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Ingår i: Springer Proceedings in Mathematics and Statistics: 3rd Annual Workshop on Inverse Problems, 2013, Stockholm, Sweden, 2-6 May 2013. - Cham : Springer International Publishing. - 2194-1009 .- 2194-1017. - 9783319124988 ; 120, s. 135-151
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Konferensbidrag (refereegranskat)abstract
- We use the conjugade gradient method for the solution of an inverse problem for simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions of the Maxwell's system in 3D using backscattering data. We show stability of our inverse problem using the Carleman estimates. Our numerical experiments show reliable reconstruction of both parameters using the optimization approach.
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| 4. |
- Beilina, Larisa, 1970, et al.
(författare)
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The layer-stripping algorithm for reconstruction of dielectrics in an optical fiber
- 2015
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Ingår i: Springer Proceedings in Mathematics and Statistics: 3rd Annual Workshop on Inverse Problems, 2013, Stockholm, Sweden, 2-6 May 2013. - Cham : Springer International Publishing. - 2194-1009 .- 2194-1017. - 9783319124988 ; 120, s. 125-134
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Konferensbidrag (refereegranskat)abstract
- We present a new model of an approximate globally convergent method in a frequency domain for reconstruction of dielectric permittivity of a weakly guiding optical fiber. We consider data which are given only at the backscattered side of the medium which should be reconstructed. We formulate new approximately globally convergent algorithm for the reconstruction of dielectric permittivity function under the assumption that the magnetic permeability is a known constant.
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| 5. |
- Beilina, Larisa, 1970, et al.
(författare)
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Time-adaptive FEM for distributed parameter identification in mathematical model of HIV infection with drug therapy
- 2015
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Ingår i: Inverse Problems and Applicationspapers from: 3rd Annual Workshop on Inverse Problems, 2013; Stockholm; Sweden; 2 - 6 May 2013; (Springer Proceedings in Mathematics & Statistics). - Cham : Springer International Publishing. - 2194-1009 .- 2194-1017. - 9783319124988 ; 120, s. 111-124
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Konferensbidrag (refereegranskat)abstract
- We propose a time-adaptive finite element method for the solution of a parameter identification problem for ODE system which describes dynamics of primary HIV infection with drug therapy. We present framework of a posteriori error estimate in the Tikhonov functional and in the Lagrangian. We also formulate the time-mesh refinement recommendation and an adaptive algorithm to find optimal values of the distributed parameter in our identification problem.
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| 6. |
- Bondestam Malmberg, John, 1988
(författare)
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A posteriori error estimate in the lagrangian setting for an inverse problem based on a new formulation of Maxwell’s system
- 2015
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Ingår i: Springer Proceedings in Mathematics and Statistics: 3rd Annual Workshop on Inverse Problems, 2013, Stockholm, Sweden, 2-6 May 2013. - Cham : Springer International Publishing. - 2194-1009 .- 2194-1017. - 9783319124988 ; 120, s. 43-53
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Konferensbidrag (refereegranskat)abstract
- In this paper we consider an inverse problem of determination of a dielectric permittivity function from a backscattered electromagnetic wave. The inverse problem is formulated as an optimal control problem for a certain partial differential equation derived from Maxwell’s system. We study a solution method based on finite element approximation and provide a posteriori error estimate for the use in an adaptive algorithm.
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| 7. |
- Karchevskii, E., et al.
(författare)
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Determination of permittivity from propagation constant measurements in optical fibers
- 2015
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Ingår i: Springer Proceedings in Mathematics and Statistics: 3rd Annual Workshop on Inverse Problems, 2013, Stockholm, Sweden, 2-6 May 2013. - Cham : Springer International Publishing. - 2194-1009 .- 2194-1017. - 9783319124988 ; 120, s. 55-65
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Konferensbidrag (refereegranskat)abstract
- We present a new method for determination of dielectric permittivity constant using measurements of fundamental mode of propagation constant in optical fiber’s. We first solve the forward spectral problem to compute the dispersion curve for the fundamental mode. Then using this curve we present an effective and accurate spline-collocation method for calculation of permittivity.
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| 8. |
- Alnefjord, Joakim, et al.
(författare)
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The Chirality-Flow Formalism for Standard Model Calculations
- 2022
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Ingår i: International Workshop on Lie Theory and Its Applications in Physics. - Singapore : Springer Nature Singapore. - 2194-1017 .- 2194-1009. - 9789811947506 ; 396, s. 387-394
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Konferensbidrag (refereegranskat)abstract
- Scattering amplitudes are often split up into their color (su(N) ) and kinematic components. Since the su(N) gauge part can be described using flows of color, one may anticipate that the su(2 ) ⊕ su(2 ) kinematic part can be described in terms of flows of chirality. In two recent papers we showed that this is indeed the case, introducing the chirality-flow formalism for standard model calculations. Using the chirality-flow method—which builds on and further simplifies the spinor-helicity formalism—Feynman diagrams can be directly written down in terms of Lorentz-invariant spinor inner products, allowing the simplest and most direct path from a Feynman diagram to a complex number. In this presentation, we introduce this method and show some examples.
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| 9. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
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A Discontinuous Galerkin Approach for Stabilized Maxwell’s Equations in Pseudo-Frequency Domain
- 2023
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Ingår i: Springer Proceedings in Mathematics and Statistics. - 2194-1009 .- 2194-1017. - 9783031358708
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Konferensbidrag (refereegranskat)abstract
- This paper concerns the study of a stabilized discontinuous Galerkin finite element method for the Maxwell’s equations in pseudo-frequency domain obtained through Laplace transformation in time. The model problem is considered in the special case assuming constant dielectric permittivity function in a boundary neighborhood. The discontinuous Galerkin finite element method (DGFEM) is formulated and the convergence is addressed in a priori setting where we derive optimal order error bound of the scheme in a L2 -based triple norm. Finally, our numerical examples confirm predicted convergence of the proposed scheme.
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| 10. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
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Adaptive approximate globally convergent algorithm with backscattered data.
- 2013
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Ingår i: Inverse Problems and Large-Scale Computations. Springer Proceedings in Mathematics and Statistics. Larisa Beilina, Yury V. Shestopalov (Eds.). - Cham : Springer International Publishing. - 2194-1009 .- 2194-1017. - 9783319006598 ; 52, s. 1-20
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Konferensbidrag (refereegranskat)abstract
- We construct, analyze and implement an approximately globally convergent finite element scheme for a hyperbolic coefficient inverse problem in the case of backscattering data. This extends the computational aspects introduced in Asadzadeh and Beilina (Inv. Probl. 26, 115007, 2010), where using Laplace transformation, the continuous problem is reduced to a nonlinear elliptic equation with a gradient dependent nonlinearity. We investigate the behavior of the nonlinear term and discuss the stability issues as well as optimal a posteriori error bounds, based on an adaptive procedure and due to the maximal available regularity of the exact solution. Numerical implementations justify the efficiency of adaptive a posteriori approach in the globally convergent setting.
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