| 1. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
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The discrete ordinates method for the neutron transport equation in an infinite cylindrical domain
- 1992
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Ingår i: Mathematical Models and Methods in Applied Science. ; 2:3, s. 317-338
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Tidskriftsartikel (refereegranskat)abstract
- We prove a regularity result for a Fredholm integral equation with weakly singular kernel, arising in connection with the neutron transport equation in an infinite cylindrical domain. The theorem states that the solution has almost two derivatives in L1, and is proved using Besov space techniques. This result is applied in the error analysis of the discrete ordinates method for the numerical solution of the neutron transport equation. We derive an error estimate in the L1-norm for the scalar flux, and as a consequence, we obtain an error bound for the critical eigenvalue.
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| 2. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
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On adaptive finite element methods for Fredholm integral equations of the second kind
- 1994
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Ingår i: SIAM Journal on Numerical Analysis. ; 31:3, s. 831-855
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Tidskriftsartikel (refereegranskat)abstract
- A posteriors and a priori error estimates are derived for a finite element discretization of a Fredholm integral equation of the second kind. A reliable and efficient adaptive algorithm is then designed for a specific computational goal with applications to potential problems. The reliability of the algorithm is guaranteed by the a posteriors error estimate and the efficiency follows from the a priori error estimate, which shows that the a posteriors error bound is sharp
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| 3. |
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| 4. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
-
A combined discontinuous Galerkin and finite volume scheme for multi-dimensional VPFP system
- 2011
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Ingår i: AIP Conference Proceedings. 27th International Symposium on Rarefied Gas Dynamics, RGD27; Pacific Grove, CA; United States; 10 July 2011 through 15 July 2011. - : AIP. - 0094-243X .- 1551-7616. - 9780735408890 ; 1333:Part 1, s. 57-62, s. 57-62
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Konferensbidrag (refereegranskat)abstract
- We construct a numerical scheme for the multi-dimensional Vlasov-Poisson-Fokker-Planck system based on a combined finite volume (FV) method for the Poisson equation in spatial domain and the streamline diffusion (SD) and discontinuous Galerkin (DG) finite element in time, phase-space variables for the Vlasov-Fokker-Planck equation.
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| 5. |
- 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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| 6. |
- Asadzadeh, Mohammad, 1952
(författare)
-
A finite element method for the neutron transport equation in an infinite cylindrical domain
- 1998
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Ingår i: SIAM Journal on Numerical Analysis. ; 35:4, s. 1299-1314
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Tidskriftsartikel (refereegranskat)abstract
- We study the spatial discretization, in a fully discrete scheme, for the numerical solution of a model problem for the neutron transport equation in an infinite cylindrical domain. Based on using an interpolation technique in the discontinuous Galerkin finite element procedure, we derive an almost optimal error estimate for the scalar flux in the L2-norm. Combining a duality argument applied to the above result together with the previous semidiscrete error estimates for the velocity discretizations, we also obtain globally optimal error bounds for the critical eigenvalues.
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| 7. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
-
A new approach to Richardson extrapolation in the finite element method for second order elliptic problems
- 2009
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Ingår i: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 78:4, s. 1951-1973
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a nonstandard local approach to Richardson extrapolation, when it is used to increase the accuracy of the standard finite element approximation of solutions of second order elliptic boundary value problems in $ \mathbb{R}^N$, $ N \ge 2$. The main feature of the approach is that it does not rely on a traditional asymptotic error expansion, but rather depends on a more easily proved weaker a priori estimate, derived in [19], called an asymptotic error expansion inequality. In order to use this inequality to verify that the Richardson procedure works at a point, we require a local condition which links the different subspaces used for extrapolation. Roughly speaking, this condition says that the subspaces are similar about a point, i.e., any one of them can be made to locally coincide with another by a simple scaling of the independent variable about that point. Examples of finite element subspaces that occur in practice and satisfy this condition are given.
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