| 1. |
- 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. - 2194-1009 .- 2194-1017. - 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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| 2. |
- 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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| 3. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
-
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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| 4. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
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Convergence of stabilized p1 finite element scheme for time harmonic maxwell’s equations
- 2020
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Ingår i: Springer Proceedings in Mathematics and Statistics. - Cham : Springer International Publishing. - 2194-1017 .- 2194-1009. ; 328, s. 33-43
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Konferensbidrag (refereegranskat)abstract
- The paper considers the convergence study of the stabilized P1 finite element method for the time harmonic Maxwell’s equations. The model problem is for the particular case of the dielectric permittivity function which is assumed to be constant in a boundary neighborhood. For the stabilized model a coercivity relation is derived that guarantee’s the existence of a unique solution for the discrete problem. The convergence is addressed both in a priori and a posteriori settings. Our numerical examples validate obtained convergence results.
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| 5. |
- Beilina, Larisa, 1970, et al.
(författare)
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A Posteriori Error Estimates and Adaptive Error Control for Permittivity Reconstruction in Conductive Media
- 2023
-
Ingår i: Springer Proceedings in Mathematics and Statistics. - 2194-1009 .- 2194-1017. - 9783031358708
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Konferensbidrag (refereegranskat)abstract
- An inverse problem of reconstruction of the spatially distributed dielectric permittivity function in the Maxwell’s system is considered. The reconstruction method is based on the optimization approach to find stationary point of the Tikhonov functional. A posteriori estimates for the corresponding Tikhonov functional and for the reconstructed dielectric permittivity function are derived. Based on these estimates two adaptive conjugate gradient algorithms are formulated. Our numerical tests show feasibility of application of an adaptive optimization algorithm for reconstruction of dielectric permittivity function using anatomically realistic breast phantom of MRI database produced in University of Wisconsin [53].
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| 6. |
- Beilina, Larisa, 1970, et al.
(författare)
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Adaptive FEM with relaxation for a hyperbolic coefficient inverse problem
- 2013
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Ingår i: Applied Inverse Problems, Springer Proceedings in Mathematics & Statistics (Select Contributions from the First Annual Workshop on Inverse Problems, Gothenburg, Sweden, 2-3 June 2011). - New York, NY : Springer New York. - 2194-1009 .- 2194-1017. - 9781461478164 ; 48, s. 129-153
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Konferensbidrag (refereegranskat)abstract
- Recent research of publications (Beilina and Johnson, Numerical Mathematics and Advanced Applications: ENUMATH 2001, Springer, Berlin, 2001; Beilina, Applied and Computational Mathematics 1, 158-174, 2002; Beilina and Johnson, Mathematical Models and Methods in Applied Sciences 15, 23-37, 2005; Beilina and Clason, SIAM Journal on Scientific Computing 28, 382-402, 2006; Beilina, Applicable Analysis 90, 1461-1479, 2011; Beilina and Klibanov, Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems, Springer, New York, 2012; Beilina and Klibanov, Journal of Inverse and Ill-posed Problems 18, 85-132, 2010; Beilina and Klibanov, Inverse Problems 26, 045012, 2010; Beilina and Klibanov, Inverse Problems 26, 125009, 2010; Beilina et al., Journal of Mathematical Sciences 167, 279-325, 2010) have shown that adaptive finite element method presents a useful tool for solution of hyperbolic coefficient inverse problems. In the above publications improvement in the image reconstruction is achieved by local mesh refinements using a posteriori error estimate in the Tikhonov functional and in the reconstructed coefficient. In this paper we apply results of the above publications and present the relaxation property for the mesh refinements and a posteriori error estimate for the reconstructed coefficient for a hyperbolic CIP, formulate an adaptive algorithm, and apply it to the reconstruction of the coefficient in hyperbolic PDE. Our numerical examples present performance of the two-step numerical procedure on the computationally simulated data where on the first step we obtain good approximation of the exact coefficient using approximate globally convergent method of Beilina and Klibanov (Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems, Springer, New York, 2012), and on the second step we take this solution for further improvement via adaptive mesh refinements.
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| 7. |
- Beilina, Larisa, 1970, et al.
(författare)
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Adaptive finite element method in reconstruction of dielectrics from backscattered data
- 2013
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Ingår i: Applied Inverse Problems, Springer Proceedings in Mathematics & Statistics. Larisa Beilina (Ed.). - New York, NY : Springer New York. - 2194-1009 .- 2194-1017. - 9781461478157 ; 48, s. 51-73
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Konferensbidrag (refereegranskat)abstract
- The validity of the adaptive finite element method for reconstruction of dielectrics in a symmetric structure is verified on time-resolved data in two dimensions. This problem has practical interest in the reconstruction of the structure of photonic crystals or in the imaging of land mines. Dielectric permittivity, locations, and shapes/sizes of dielectric abnormalities are accurately imaged using adaptive finite element algorithm.
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| 8. |
- Beilina, Larisa, 1970, et al.
(författare)
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Approximate global convergence in imaging of land mines from backscattered data
- 2013
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Ingår i: Applied Inverse Problems, Springer Proceedings in Mathematics & Statistics (Select Contributions from the First Annual Workshop on Inverse Problems, Gothenburg, Sweden, 2-3 June 2011). - New York, NY : Springer New York. - 2194-1009 .- 2194-1017. - 9781461478164 ; 48, s. 15-36
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Konferensbidrag (refereegranskat)abstract
- We present new model of an approximate globally convergent method in the most challenging case of the backscattered data. In this case data for the coefficient inverse problem are given only at the backscattered side of the medium which should be reconstructed. We demonstrate efficiency and robustness of the proposed technique on the numerical solution of the coefficient inverse problem in two dimensions with the time-dependent backscattered data. Goal of our tests is to reconstruct dielectrics in land mines which is the special case of interest in military applications. Our tests show that refractive indices and locations of dielectric abnormalities are accurately imaged.
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| 9. |
- Beilina, Larisa, 1970, et al.
(författare)
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Convergence of explicit p1 Finite-Element Solutions to Maxwell’s Equations
- 2020
-
Ingår i: Springer Proceedings in Mathematics and Statistics. - Cham : Springer International Publishing. - 2194-1017 .- 2194-1009. ; 328, s. 91-103
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Konferensbidrag (refereegranskat)abstract
- This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell’s equations in terms of the sole electric field. The space discretization is performed by the standard P1 finite element method assorted with the treatment of the time-derivative term by a technique of the mass-lumping type. The rigorous reliability analysis of this numerical model was the subject of authors’ another paper [2]. More specifically such a study applies to the particular case where the electric permittivity has a constant value outside a sub-domain, whose closure does not intersect the boundary of the domain where the problem is defined. Our numerical experiments in two-dimension space certify that the convergence results previously derived for this approach are optimal, as long as the underlying CFL condition is satisfied.
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| 10. |
- Beilina, Larisa, 1970, et al.
(författare)
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Methods of Quantitative Reconstruction for Acoustic Coefficient Inverse Problem
- 2023
-
Ingår i: Springer Proceedings in Mathematics and Statistics. - 2194-1017 .- 2194-1009. - 9783031358708 ; 429, s. 167-198
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Konferensbidrag (refereegranskat)abstract
- The paper considers an inverse problem of reconstructing the spatially distributed wave speed function in an acoustic wave equation using backscattered data. Three different reconstruction methods are discussed: the method of analytic reconstruction, adaptive finite element inversion method and the adaptive spectral inversion method. We present numerical examples which show the performance of the different inverse algorithms, and compare the reconstructions obtained by those three methods.
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