scholarly journals SWAPS-AN EXPERIMENTAL PROGRAM FOR NUMERICAL SOLUTION OF THE TRANSPORT EQUATION WITH ANISOTROPIC SCATTERING IN ONE-DIMENSIONAL SLAB GEOMETRY

1962 ◽  
Author(s):  
M.L. Tobias ◽  
T.B. Fowler
Keyword(s):  
Numerical Solution ◽  
Transport Equation ◽  
Anisotropic Scattering ◽  
Experimental Program ◽  
Slab Geometry ◽  
One Dimensional

Solution of the Transport Equation with Anisotropic Scattering in Slab Geometry

1968 ◽  
Vol 9 (5) ◽  
pp. 753-759 ◽  
Author(s):  
Robert L. Bowden ◽  
F. Joseph McCrosson ◽  
Edgar A. Rhodes
Keyword(s):  
Transport Equation ◽  
Anisotropic Scattering ◽  
Slab Geometry

Error analysis and uncertainty quantification for the heterogeneous transport equation in slab geometry

2020 ◽  
Author(s):  
Ivan G Graham ◽  
Matthew J Parkinson ◽  
Robert Scheichl
Keyword(s):  
Monte Carlo ◽  
Error Analysis ◽  
Error Estimate ◽  
Transport Equation ◽  
Uncertainty Quantification ◽  
Cross Sections ◽  
Dimensional Space ◽  
Slab Geometry ◽  
One Dimensional ◽  
Bochner Space

Abstract We present an analysis of multilevel Monte Carlo (MLMC) techniques for the forward problem of uncertainty quantification for the radiative transport equation, when the coefficients (cross-sections) are heterogenous random fields. To do this we first give a new error analysis for the combined spatial and angular discretisation in the deterministic case, with error estimates that are explicit in the coefficients (and allow for very low regularity and jumps). This detailed error analysis is done for the one-dimensional space–one-dimensional angle slab-geometry case with classical diamond differencing. Under reasonable assumptions on the statistics of the coefficients, we then prove an error estimate for the random problem in a suitable Bochner space. Because the problem is not self-adjoint, stability can only be proved under a path-dependent mesh resolution condition. This means that, while the Bochner space error estimate is of order $\mathcal{O}(h^{\eta })$ for some $\eta $ where $h$ is a (deterministically chosen) mesh diameter, smaller mesh sizes might be needed for some realisations. We also show that the expected cost for computing a typical quantity of interest remains of the same order as for a single sample. This leads to rigorous complexity estimates for Monte Carlo (MC) and MLMC: for particular linear solvers, the multilevel version gives up to two orders of magnitude improvement over MC. We provide numerical results supporting the theory.

About the FN Approximation to Fractional Neutron Transport Equation in Slab Geometry

2011 ◽  
Author(s):  
Dumitru Baleanu ◽  
Abdelouahab Kadem
Keyword(s):  
Transport Equation ◽  
Polynomial Approximation ◽  
Approximation Method ◽  
Legendre Polynomial ◽  
Neutron Transport ◽  
Neutron Transport Equation ◽  
Slab Geometry ◽  
One Dimensional ◽  
The One

The neutron transport denotes the study of the motions and interactions of neutrons with materials. In given applications we need to know where neutrons are in an apparatus, what direction they are moving, and how fast they are going. In this manuscript the Legendre polynomial approximation method FN was applied to the one dimensional slab geometry neutron transport equation.

General Eigenvalue Spectrum in a One-Dimensional Slab Geometry Transport Equation

2005 ◽  
Vol 150 (1) ◽  
pp. 72-77 ◽  
Author(s):  
Fikret Anli ◽  
Faruk Yasa ◽  
Süleyman Güngör
Keyword(s):  
Transport Equation ◽  
Eigenvalue Spectrum ◽  
Slab Geometry ◽  
One Dimensional
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