| 1. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
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A posteriori error estimates in a globally convergent FEM for a hyperbolic coefficient inverse problem
- 2010
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Ingår i: Inverse Problems. - : IOP Publishing. - 0266-5611 .- 1361-6420. ; 26:11
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Tidskriftsartikel (refereegranskat)abstract
- This study concerns a posteriori error estimates in a globally convergent numerical method for a hyperbolic coefficient inverse problem. Using the Laplace transform the model problem is reduced to a nonlinear elliptic equation with a gradient dependent nonlinearity. We investigate the behavior of the nonlinear term in both a priori and a posteriori settings and derive optimal a posteriori error estimates for a finite-element approximation of this problem. Numerical experiments justify the efficiency of a posteriori estimates in the globally convergent approach.
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| 2. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
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A Priori Error Estimates and Computational Studies for a Fermi Pencil-Beam Equation
- 2018
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Ingår i: Journal of Computational and Theoretical Transport. - : Informa UK Limited. - 2332-4325 .- 2332-4309. ; 47:1-3, s. 125-151
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Tidskriftsartikel (refereegranskat)abstract
- We derive a priori error estimates for the standard Galerkin and streamline diffusion finite element methods for the Fermi pencil-beam equation obtained from a fully three-dimensional Fokker-Planck equation in space and velocity variables. For a constant transport cross-section, there is a closed form analytic solution available for the Fermi equation with a data as product of Dirac functions. Our objective is to study the case of nonconstant, nonincreasing transport cross-section. Therefore we start with a theoretical, that is, a priori, error analysis for a Fermi model with modified initial data in L-2. Then we construct semi-streamline-diffusion and characteristic streamline-diffusion schemes and consider an adaptive algorithm for local mesh refinements. To derive the stability estimates, for simplicity, we rely on the assumption of nonincreasing transport cross-section. Different numerical examples, in two space dimensions are justifying the theoretical results. Implementations show significant reduction of the computational error by using such adaptive procedure.
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| 3. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
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A stabilized P1 domain decomposition finite element method for time harmonic Maxwell's equations
- 2023
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Ingår i: Mathematics and Computers in Simulation. - : Elsevier BV. - 0378-4754. ; 204, s. 556-574
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Tidskriftsartikel (refereegranskat)abstract
- One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations is to render their hyperbolic character to elliptic form. This paper is devoted to the study of a stabilized linear, domain decomposition, finite element method for the time harmonic Maxwell's equations, in a dual form, obtained through the Laplace transformation in time. The model problem is for the particular case of the dielectric permittivity function which is assumed to be constant in a boundary neighborhood. The discrete problem is coercive in a symmetrized norm, equivalent to the discrete norm of the model problem. This yields discrete stability, which together with continuity guarantees the well-posedness of the discrete problem, cf Arnold et al. (2002) [3], Di Pietro and Ern (2012) [45]. The convergence is addressed both in a priori and a posteriori settings. In the a priori error estimates we confirm the theoretical convergence of the scheme in a L2-based, gradient dependent, triple norm. The order of convergence is O(h) in weighted Sobolev space Hw2(ohm), and hence optimal. Here, the weight w := w(epsilon, s) where epsilon is the dielectric permittivity function and s is the Laplace transformation variable. We also derive, similar, optimal a posteriori error estimates controlled by a certain, weighted, norm of the residuals of the computed solution over the domain and at the boundary (involving the relevant jump terns) and hence independent of the unknown exact solution. The a posteriori approach is used, e.g. in constructing adaptive algorithms for the computational purposes, which is the subject of a forthcoming paper. Finally, through implementing several numerical examples, we validate the robustness of the proposed scheme. (c) 2022 The Author(s). Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS). This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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| 4. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
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Stability and Convergence Analysis of a Domain Decomposition FE/FD Method for Maxwell's Equations in the Time Domain
- 2022
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Ingår i: Algorithms. - : MDPI AG. - 1999-4893. ; 15:10
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Tidskriftsartikel (refereegranskat)abstract
- Stability and convergence analyses for the domain decomposition finite element/finite difference (FE/FD) method are presented. The analyses are developed for a semi-discrete finite element scheme for time-dependent Maxwell's equations. The explicit finite element schemes in different settings of the spatial domain are constructed and a domain decomposition algorithm is formulated. Several numerical examples validate convergence rates obtained in the theoretical studies.
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| 5. |
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| 6. |
- Beilina, Larisa, 1970, et al.
(författare)
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A new approximate mathematical model for global convergence for a coefficient inverse problem with backscattering data
- 2012
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Ingår i: Journal of Inverse and Ill-Posed Problems. - : Walter de Gruyter GmbH. - 0928-0219 .- 1569-3945. ; 20:4, s. 513-565
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Tidskriftsartikel (refereegranskat)abstract
- An approximately globally convergent numerical method for a 3d coefficient inverse problem for a hyperbolic equation with backscattering data is presented. A new approximate mathematical model is presented as well. An approximation is used only on the first iteration and amounts to the truncation of a certain asymptotic series. A significantly new element of the convergence analysis is that the so-called "tail functions" are estimated. Numerical results in 2d and 3d cases are discussed, including the one for a quite heterogeneous medium.
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