Finite element, nodal and response matrix methods: A variational synthesis for neutron transport

Lewis, E.E.; Dilber, I.

doi:10.1016/0149-1970(86)90013-2

Cited by 12 publications

(2 citation statements)

References 7 publications

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“…At core scale, APOLLO3® offers several numerical solvers to solve the Boltzmann equation: MINOS (Baudron et al, 2007), PASTIS (Lewis et al, 1986) and MINARET (Moller et al, 2011). Among them -which are equally efficient to master flux calculation for depletion purpose -MINOS and PASTIS are not able to manage unstructured geometries.…”

Section: The Modelling Of the Irradiationmentioning

confidence: 99%

Validation of fast neutron reactors fertile blanket depletion calculations through the analysis of the DOUBLON experiment in Phenix with TRIPOLI-4® and DARWIN3-SFR

Calame

Lebrat

Buiron

2022

Annals of Nuclear Energy

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Section: The Modelling Of the Irradiationmentioning

confidence: 99%

Validation of fast neutron reactors fertile blanket depletion calculations through the analysis of the DOUBLON experiment in Phenix with TRIPOLI-4® and DARWIN3-SFR

Calame

Lebrat

Buiron

2022

Annals of Nuclear Energy

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“…It uses an integral form of Eqs. (6) and applies response-matrix approach [15,16] to formulate of the equations for the scalar flux in l-th subdomain…”

Section: Introductionmentioning

confidence: 99%

Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme

Anistratov

Azmy

2015

Journal of Computational Physics

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We study convergence of the integral transport matrix method (ITMM) based on a parallel block Jacobi (PBJ) iterative strategy for solving particle transport problems. The ITMM is a spatial domain decomposition method proposed for massively parallel computations. A Fourier analysis of the PBJ-based iterations applied to S N diamond-difference equations in 1D slab and 2D Cartesian geometries is performed. It is carried out for infinite-medium problems with homogeneous material properties. To analyze the performance of the ITMM with the PBJ algorithm and evaluate its potential in scalability we consider a limiting case of one spatial cell per subdomain. The analysis shows that in such limit the spectral radius of the iteration method is one without regard to values of the scattering ratio and optical thickness of the spatial cells. This implies lack of convergence in infinite medium. Numerical results of finite-medium problems are presented. They demonstrate effects of finite size of spatial domain on the performance of the iteration algorithm as well as its asymptotic behavior when the extent of the spatial domain increases. These numerical experiments also show that for finite domains iterative convergence to a finite criterion is achievable in a multiple of the sum of number of cells in each dimension.

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Variational nodal transport solutions of multigroup criticality problems

Carrico

Lewis

1991

Progress in Nuclear Energy

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Finite element, nodal and response matrix methods: A variational synthesis for neutron transport

Cited by 12 publications

References 7 publications

Validation of fast neutron reactors fertile blanket depletion calculations through the analysis of the DOUBLON experiment in Phenix with TRIPOLI-4® and DARWIN3-SFR

Validation of fast neutron reactors fertile blanket depletion calculations through the analysis of the DOUBLON experiment in Phenix with TRIPOLI-4® and DARWIN3-SFR

Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme

Variational nodal transport solutions of multigroup criticality problems

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