Stability analysis of nonlinear two-grid method for multigroup neutron diffusion problems

Anistratov, Dmitriy Y.; Cornejo, Luke R.; Jones, Jesse P.

doi:10.1016/j.jcp.2017.06.014

Cited by 7 publications

(3 citation statements)

References 19 publications

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“…The RHS of Eq. ( 3) is formulated using the multiplicative correction factor ζ that is defined by the solution of the multigroup and grey LOSM equations [9,11]. This form of the RHS introduces nonlinearity in the multigroup LOSM equations.…”

Section: Multilevel Second-moment Methodsmentioning

confidence: 99%

Multilevel Second-Moment Methods with Group Decomposition for Multigroup Transport Problems

Anistratov,

Coale,

Warsa

et al. 2021

Preprint

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This paper presents multilevel iterative schemes for solving the multigroup Boltzmann transport equations (BTEs) with parallel calculation of group equations. They are formulated with multigroup and grey low-order equations of the Second-Moment (SM) method. The group high-order BTEs and low-order SM (LOSM) equations are solved in parallel. To further improve convergence and increase computational efficiency of algorithms Anderson acceleration is applied to inner iterations for solving the system of multigroup LOSM equations. Numerical results are presented to demonstrate performance of the multilevel iterative methods.

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Section: Multilevel Second-moment Methodsmentioning

confidence: 99%

Multilevel Second-Moment Methods with Group Decomposition for Multigroup Transport Problems

Anistratov,

Coale,

Warsa

et al. 2021

Preprint

Self Cite

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“…And there are many authors and researchers who discussed stability of the iterative sequence generated by the algorithm for solving the investigated problems. See, for example, [11,37] and the references therein. Recently, convergence and stability theorems for the Picard-Mann iterative scheme of iteration are attracting more and more attention in researches.…”

Section: Andmentioning

confidence: 99%

On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and Applications

Lan

2019

Journal of Function Spaces

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In order to solve (partial) differential equations, implicit midpoint rules are often employed as a powerful numerical method. The purpose of this paper is to introduce and study a class of new Picard-Mann iteration processes with mixed errors for the implicit midpoint rules, which is different from existing methods in the literature, and to analyze the convergence and stability of the proposed method. Further, some numerical examples and applications to optimal control problems with elliptic boundary value constraints are considered via the new Picard-Mann iterative approximations, which shows that the new Picard-Mann iteration process with mixed errors for the implicit midpoint rule of nonexpansive mappings is brand new and more effective than other related iterative processes.

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“…Thus, there are many scholars and researchers who have discussed stability of the iterative sequence generated by the algorithm for solving the investigated problems. See, for example, [23][24][25][26][27] and the references therein. Especially, stimulated by the work of Bosede and Rhoades [28], Akewe and Okeke [27] obtained stability results for the Picard-Mann hybrid iterative scheme due to Khan [18] for a general class of contractive-like operators introduced by Bosede and Rhoades [28].…”

Section: Introductionmentioning

confidence: 99%

New approximation methods for solving elliptic boundary value problems via Picard-Mann iterative processes with mixed errors

Lan

2017

Bound Value Probl

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In this paper, we introduce and study a class of new Picard-Mann iterative methods with mixed errors for common fixed points of two different nonexpansive and contraction operators. We also give convergence and stability analysis of the new Picard-Mann iterative approximation and propose numerical examples to show that the new Picard-Mann iteration converges more effectively than the Picard iterative process, Mann iterative process, Picard-Mann iterative process due to Khan and other related iterative processes. Furthermore, as an application, we explore iterative approximation of solutions for an elliptic boundary value problem in Hilbert spaces by using the new Picard-Mann iterative methods with mixed errors for contraction operators. MSC: 47H10; 54H25; 47H09

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Stability analysis of nonlinear two-grid method for multigroup neutron diffusion problems

Cited by 7 publications

References 19 publications

Multilevel Second-Moment Methods with Group Decomposition for Multigroup Transport Problems

Multilevel Second-Moment Methods with Group Decomposition for Multigroup Transport Problems

On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and Applications

New approximation methods for solving elliptic boundary value problems via Picard-Mann iterative processes with mixed errors

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