Linear triangle finite element formulation for multigroup neutron transport analysis with anisotropic scattering

Lillie, R.A.; Robinson, J.C.

doi:10.2172/7184163

Cited by 6 publications

(4 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the anisotropic scattering case does not require conceptually new insights. Using the even-parity approach, the forward problem has already been solved for anisotropic scattering in one and two dimensions by Kaplan and Davis, 32 Lillie and Robinson, 46 and Oliveira. 33 The fundamental structure of the equations for the inverse problem ͓Eqs.…”

Section: Discussionmentioning

confidence: 99%

Three-dimensional optical tomography with the equation of radiative transfer

Abdoulaev

2003

J. Electron. Imaging

View full text Add to dashboard Cite

We report on the derivation and implementation of the first three-dimensional optical tomographic image reconstruction scheme that is based on the time-independent equation of radiative transfer (ERT) and allows for arbitrarily shaped medium boundaries and arbitrary spatial material distributions. The scheme builds on the concept of model-based iterative image reconstruction, in which a forward model provides prediction of detector readings, and a gradient-based updating scheme minimizes an appropriately defined objective function. The forward model is solved by using an even-parity formulation of the ERT, which lends itself to a finiteelement discretization method. The finite-element technique provides the suitable framework for predicting light propagation in arbitrarily shaped three-dimensional media. For an efficient way of calculating the gradient of the objective function we have implemented an adjoint differentiation scheme. Initial reconstruction results using synthetic data from simple media and a threedimensional mesh of the human forehead illustrate the performance of the code.

show abstract

Section: Discussionmentioning

confidence: 99%

Three-dimensional optical tomography with the equation of radiative transfer

Abdoulaev

2003

J. Electron. Imaging

View full text Add to dashboard Cite

show abstract

“…Use of specular reflection boundary conditions common to transport problems also complicates the formulation, and forces an implicit solution in the numerical implementation rather than the preferred iterative solution. 3 Lillie and Robinson 18 have developed an even-parity finite element model which incorporates anisotropic scattering, but the computational efficiency of this method is unattractive relative to simpler and significantly faster finite difference approaches. Because of the time and storage requirements for this approach, it cannot be effectively applied in large complicated problems.…”

Section: Finite Element Methodsmentioning

confidence: 99%

“…Intracell relationships, or the relationship between the fluxes on the sides of each cell, are represented by the term γ ij of Eq. (18). In order to calculate this term, one must first determine the lengths s 1 , s 2 , £ i and L j .…”

Section: Intracell Relationshipsmentioning

confidence: 99%

See 1 more Smart Citation

A discrete ordinates approximation to the neutron transport equation applied to generalized geometries

DeHart¹

1992

View full text Add to dashboard Cite

A method for applying the discrete ordinates method for solution of the neutron transport equation in arbitrary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the traditional shape of a mesh element within a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. Using the method developed here, a general two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons.The method of characteristics, originally developed to eliminate negative fluxes encountered in many finite difference approximations, had been previously applied to regular cell structures in multiple dimensions and various coordinate systems. In such geometries, the geometrical relationships between sides were determined analytically and incorporated directly into the numerical model. However, the present work makes no assumptions about the orientations or the number of sides in a given cell, and computes all geometric relationships between each set of sides in each cell for each discrete direction. A set of nonreentrant polygons can therefore be used to represent any given two-dimensional space.iv Results for a number of test problems have been compared to solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN computer programs. Numerical results were obtained for problems ranging from simple onedimensional geometry to complicated multidimensional configurations. These results have demonstrated the ability of the developed method to closely approximate complex geometrical configurations and to obtain accurate results for problems that are extremely difficult to model using traditional methods. v DEDICATION This work is dedicated to my wife, Leigh. Her patience, understanding and love over the long road leading to this point made the path seem much less rocky; her encouragement and willingness to listen to my problems helped to sustain my efforts; and the daughter she has given us has taught me that miracles are possible. vi ACKNOWLEDGEMENTS I wish to express my sincere and profound gratitude to Ron Pevey and Ted Parish, both of whom provided invaluable support and insight in my endeavors. Their guidance, encouragement, technical assistance and senses of humor were invaluable assets. I also wish to acknowledge the support given to me by the United States Department of Energy, the Westinghouse Savannah River Company, and most importantly, by several members of my direct management and by my colleagues within the Savannah Riv...

show abstract