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- Asadzadeh, Mohammad, 1952, et al.
(author)
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A posteriori error estimates in a globally convergent FEM for a hyperbolic coefficient inverse problem
- 2010
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In: Inverse Problems. - : IOP Publishing. - 0266-5611 .- 1361-6420. ; 26:11
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Journal article (peer-reviewed)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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| 3. |
- Asadzadeh, Mohammad, 1952, et al.
(author)
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Asymptotic error expansions for the finite element method for second order elliptic problems in R_N, N>=2, I: Local interior expansions
- 2010
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In: SIAM Journal on Numerical Analysis. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1429 .- 1095-7170. ; 48:5, s. 2000-2017
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Journal article (peer-reviewed)abstract
- Our aim here is to give sufficient conditions on the finite element spaces near a point so that the error in the finite element method for the function and its derivatives at the point have exact asymptotic expansions in terms of the mesh parameter h, valid for h sufficiently small. Such expansions are obtained from the so-called asymptotic expansion inequalities valid in RN for N ≥ 2, studies by Schatz in [Math. Comp., 67 (1998), pp. 877-899] and [SIAM J. Numer. Anal., 38 (2000), pp. 1269-1293].
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| 6. |
- Asadzadeh, Mohammad, 1952, et al.
(author)
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Galerkin methods for primary ion transport in inhomogeneous media
- 2010
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In: Kinetic and Related Models. - : American Institute of Mathematical Sciences (AIMS). - 1937-5093 .- 1937-5077. ; 3:3, s. 373-394
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Journal article (peer-reviewed)abstract
- This paper concerns the energy deposition of high-energy (e.g., approximate to 50 - 500 MeV) proton and carbon ions and high-energy electrons (of approximate to 50 MeV), in inhomogeneous media. Our goal is to develop a flexible model incorporated with the analytic theory for ions based on bipartition and Fokker-Planck developments. Both procedures are leading to convection dominated convection diffusion equations. We study convergence for semi-discrete and fully discrete approximations of a such obtained equation, for abroad beam model, using the standard Galerkin and streamline diffusion finite element methods. The analytic broad beam model of the light ion absorbed dose were compared with the results of the modified Monte Carlo (MC) code SHIELD-HIT+ and those of Galerkin streamline diffusion approach.
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| 7. |
- Asadzadeh, Mohammad, 1952, et al.
(author)
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Ion transport in inhomogeneous media based on the bipartition model for primary ions
- 2010
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In: Computers & Mathematics with Applications. - : Elsevier BV. - 0898-1221. ; 60:8, s. 2445-2459
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Journal article (peer-reviewed)abstract
- The present paper is focused on the mathematical modeling of the charged particle transport in nonuniform media. We study the energy deposition of high energy protons and electrons in an energy range of approximate to 50-500 MeV. This work is an extension of the bipartition model; for high energy electrons studied by Luo and Brahme in [Z. Luo, A. Brahme, High energy electron transport, Phys. Rev. B 46 (1992) 739-752] [42]; and for light ions studied by Luo and Wang in [Z. Luo, S. Wang, Bipartition model of ion transport: an outline of new range theory for light ions, Phys. Rev. B 36 (1987) 1885-1893]; to the field of high energy ions in inhomogeneous media with the retained energy-loss straggling term. In the bipartition model, the transport equation is split into a coupled system of convection diffusion equations controlled by a partition condition. A similar split is obtained in an asymptotic expansion approach applied to the linear transport equation yielding pencil beam and broad beam models, which are again convection diffusion type equations. We shall focus on the bipartition model applied for solving three types of problems: (i) normally incident ion transport in a slab; (ii) obliquely incident ion transport in a semi-infinite medium; (iii) energy deposition of ions in a multilayer medium. The broad beam model of the proton absorbed dose was illustrated with the results of a modified Monte Carlo code: SHIELD - HIT+.
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| 8. |
- Asadzadeh, Mohammad, 1952, et al.
(author)
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On discontinuous Galerkin and discrete ordinates approximations for neutron transport equation and the critical eigenvalue.
- 2010
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In: Nuovo Cimento della Societa Italiana di Fisica C. - 1124-1896. ; 33:1, s. 21-29
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Journal article (peer-reviewed)abstract
- The objective of this paper is to give a mathematical framework for a fully discrete numerical approach for the study of the neutron transport equation in a cylindrical domain (container model,). More specifically, we consider the discontinuous Galerkin (DG) finite element method for spatial approximation of the mono-energetic, critical neutron transport equation in an infinite cylindrical domain ω̃in R3 with a polygonal convex cross-section ω The velocity discretization relies on a special quadrature rule developed to give optimal estimates in discrete ordinate parameters compatible with the quasi-uniform spatial mesh. We use interpolation spaces and derive optimal error estimates, up to maximal available regularity, for the fully discrete scalar flux. Finally we employ a duality argument and prove superconvergence estimates for the critical eigenvalue.
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