49
Views
0
CrossRef citations to date
0
Altmetric
Technical Paper

Preconditioned Krylov Solution of Response Matrix Equations

, , , &
Pages 222-232 | Published online: 17 Mar 2017

REFERENCES

  • R. J. PRYOR, “Recent Developments in the Response Matrix Method,” Advances in Reactors: Physics, Design and Economics, J. M. KALLFELZ and R. A. KARAM, Eds., Pergamon Press, New York (1975).
  • S. LINDAHL and Z. WEISS, “The Response Matrix Method,” Adv. Nucl. Sci. Technol., 13, 72 (1981).
  • E. Z. MULLER and Z. J. WEISS, “Benchmarking with the Multigroup Diffusion High Order Response Matrix Method,” Ann. Nucl. Energy, 18, 535 (1991).
  • W. S. YANG, “Response Matrix Properties and Convergence Implications for an Interface-Current Nodal Formulation,” Nucl. Sci. Eng., 121, 416 (1995).
  • E. M. MALAMBER and E. H. MUND, “ASelfConsistent Nodal Method in Response Matrix Formalism for the Multigroup Diffusion Equations,” Ann. Nucl. Energy, 23, 99 (1996).
  • K. TADA et al., “Validation of Neutron Current Formulations for the Response Matrix Method Based on the SP3 Theory,” Ann. Nucl. Energy, 37, 22 (2010).
  • G. COSSA, V. GIUSTI, and B. MONTAGNINI, “ABoundary Element-Response Matrix Method for Criticality Diffusion Problems in XYZ Geometry,” Ann. Nucl. Energy, 37, 953 (2010).
  • C. B. CARRICO, E. E. LEWIS, and G. PALMIOTTI, “Three-Dimensional Variational Nodal Transport Methods for Cartesian, Triangular, and Hexagonal Criticality Calculations,” Nucl. Sci. Eng., 111, 168 (1992).
  • G. PALMIOTTI, E. E. LEWIS, and C. B. CARRICO, “VARIANT: VARIational Anisotropic Nodal Transport for Multidimensional Cartesian and Hexagonal Geometry Calculation,” ANL-95/40, Argonne National Laboratory (1995).
  • E. E. LEWIS and G. PALMIOTTI, “Red-Black Response Matrix Acceleration by Transformation of Interface Variables,” Nucl. Sci. Eng., 130, 181 (1998).
  • M. A. SMITH et al., “Higher Order Angular Capabilities of the VARIANT Code,” Trans. Am. Nucl. Soc., 86, 321 (2002).
  • M. A. SMITH et al., “AFinite Subelement Generalization of the Variational Nodal Method,” Nucl. Sci. Eng., 144, 36 (2003).
  • E. E. LEWIS, M. A. SMITH, and G. PALMIOTTI, “A New Paradigm for Local-Global Coupling in Whole-Core Neutron Transport,” Nucl. Sci. Eng., 161, 279 (2009).
  • Y. SAAD, Iterative Methods for Sparse Linear Systems, 2nd ed., Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania (2003).
  • B. W. PATTON and J. P. HOLLOWAY, “Application of Preconditioned GMRES to the Numerical Solution of the Neutron Transport Equation,” Ann. Nucl. Energy, 29, 109 (2001).
  • J. S. WARSA et al., “Krylov Subspace Iterations for Deterministic k-Eigenvalue Calculations,” Nucl. Sci. Eng., 147, 26 (2004).
  • E. W. LARSEN and J. E. MOREL, “Advances in Discrete-Ordinates Methodology,” Nuclear Computational Science: A Century in Review, Y. AZMY and E. SARTORI, Eds., Springer, Dordrecht, The Netherlands (2010).
  • E. E. LEWIS et al., “Response Matrix Acceleration Methods Based on Orthogonalization and Domain Decomposition,” Trans. Am. Nucl. Soc., 102, 540 (2010).
  • E. E. LEWIS et al., “Comparison of Krylov andp-Multigrid Solutions of Orthogonal Response Matrix Equations,” Trans. Am. Nucl. Soc., 102, 538 (2010).
  • E. E. LEWIS et al., “Preconditioned Krylov and Gauss-Seidel Solutions of Response Matrix Equations,” Proc. Int. Conf. Mathematics, Computational Methods and Reactor Physics, Rio de Janeiro, Brazil, May 8–12, 2011.
  • Y. LI, E. E. LEWIS, and M. A. SMITH, “A p Preconditioned GMRES Algorithm for Multigroup Variational Nodal Eigenvalue Problems,” Trans. Am. Nucl. Soc., 105, 508 (2011).
  • Y. SAAD andM. H. SCHULTZ, “GMRES:AGeneralized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems,” SIAM J. Sci. Stat. Comput., 7, 856 (1986).
  • W. E. ARNOLDI, “The Principle of Minimized Iteration in the Solution of the Matrix Eigenvalue Problem,” Q. Appl. Math, 9, 17 (1951).
  • B. SMITH, P. BJORSTAD, and W. GROPP, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press, New York (1966).
  • W. L. BRIGGS, V. E. HENSON, and S. F. McCORMICK, A Multigrid Tutorial, 2nd ed., Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania (2000).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.