The Boundary Source Method with Arbitrary Order Anisotropic Scattering

REFERENCES

• M. R. WAGNER, “Three-Dimensional Nodal Diffusion and Transport Theory Methods for Hexagonal-z Geometry,” Nucl. Sci. Eng., 103, 377 (1989).
   Web of Science ®Google Scholar
• R. BEAUWENS, J. DEVOOGHT, E. MUND, R. RYDIN, and M. WAGNER, “A 3D Multigroup Transport Kinetics Code in Hexagonal Geometry for Fast Reactor Transient Analysis,” Proc. Int. Conf. Physics of Reactors: Operation, Design and Computation (PHYSOR 90), Marseille, France, April 23–27, 1990, p. XII.11, American Nuclear Society (1990).
   Google Scholar
• R. BEAUWENS and A. VAN DE VELDE, “A Higher Order Hexagonal-Z Nodal Transport Method,” Transp. Theory Stat. Phys., 24, 133 (1995).
   Google Scholar
• H. A. ABDERRAHIM, P. KUPSCHUS, E. MALAMBU, P. BENOIT, K. VAN TICHELEN, B. ARIEN, F. VERMEERSCH, Y. JONGEN, S. TERNIER, and D. VANDEPLASSCHE, “MYRRHA: A Multipurpose Accelerator Driven System for Research & Development,” Nucl. Instrum. Methods Phys. Res. A, 463, 487 (2001).
   Web of Science ®Google Scholar
• H. A. ABDERRAHIM et al., “MYRRHA Pre-Design File— Draft 2,” R-4234, SCKCEN (2005).
   Google Scholar
• B. MONTAGNINI and V. PIERPAOLI, “Il metodo delle sorgenti superficiali,” Technical Report Fisica del Reattore, Consiglio Nazionale delle Ricerche, Roma (1965).
   Google Scholar
• R. BEAUWENS and J. DEVOOGHT, “Etude du transport des neutrons en milieu hétérogène à une vitesse par la méthode des sources superficielles,” Proc. Conf. Advances in Reactor Theory, pp. 2,1–2,37, Karlsruhe, Germany, June 27–29, 1966, European Atomic Energy Society (1966).
   Google Scholar
• R. BEAUWENS and J. DEVOOGHT, “The Study of One-Speed Multiregion Transport Problems in Plane Geometry by the Method of Boundary Sources,” Nucl. Sci. Eng., 32, 249 (1968).
   Web of Science ®Google Scholar
• N. LALETIN, “The Method of Fictitious Boundary Sources for Solving the Neutron Transport Equation,” IAE-1374, Institute for Atomic Energy, Moscow (1967) (in Russian).
   Google Scholar
• P. BENOIST and A. KAVENOKY, “La méthode Cn d’approximation de l’équation de Boltzmann,” CEA-R-3170, Commissariat à l’Energie Atomique (1968).
   Google Scholar
• P. BENOIST and A. KAVENOKY, “A New Method of Approximation of the Boltzmann Equation,” Nucl. Sci. Eng., 32, 225 (1968).
   Web of Science ®Google Scholar
• P. BENOIST and A. KAVENOKY, “The Cn Method of Approximating the Boltzmann Equation in Cylindrical Geometry,” Nucl. Sci. Eng., 32, 270 (1968).
   Web of Science ®Google Scholar
• R. BEAUWENS and P. HALLET, “The Method of Boundary Sources in Cylindrical Geometry,” Technical Report, Université Libre de Bruxelles, Brussels (1973).
   Google Scholar
• N. LALETIN, N. SULTANOV, A. VLASOV, and S. KONIAEV, “The Effect of the Anisotropic Scattering on the Thermal Utilization Factor,” Ann. Nucl. Sci. Eng., 1, 333 (1974).
   Web of Science ®Google Scholar
• N. LALETIN, “Analysis of the Surface Pseudosources Method (Gn Approximations) and Comparison with Other Numerical Methods for the Neutron Transport Equation,” Transp. Theory Stat. Phys., 27, 639 (1998).
   Google Scholar
• G. VAN DEN EYNDE, “Neutron Transport with Anisotropic Scattering,” PhD Thesis, Université Libre de Bruxelles (2005).
   Google Scholar
• J. MIKA, “Neutron Transport with Anistropic Scattering,” Nucl. Sci. Eng., 11, 415 (1961).
   Web of Science ®Google Scholar
• K. CASE and P. ZWEIFEL, Linear Transport Theory, Addison-Wesley Publishing Company, Boston, Massachusetts (1967).
   Google Scholar
• B. MONTAGNINI, “Case Eigenfunctions for Pedestrians,” Nuclear Reactor Physics: A Collection of Papers Dedicated to Silvio Edoardo Corno, p. 11, Cooperativa Libraria Univeritaria Torinese (2005).
   Google Scholar
• G. GOLUB and C. VAN LOAN, Matrix Computations, 3rd ed., The John Hopkins University Press, Baltimore, Maryland (1996).
   Google Scholar
• K.-C. TOH and L. TREFETHEN, “Pseudozeros of Polynomials and Pseudospectra of Companion Matrices,” Numerische Mathematik, 68, 403 (1994).
   Web of Science ®Google Scholar
• R. CLINT WHALEY and ANTOINE PETITET, “Minimizing Development and Maintenance Costs in Supporting Persistently Optimized BLAS,” Software: Practice and Experience, 35, 2, 101 (2005).
   Web of Science ®Google Scholar
• E. ANDERSON, Z. BAI, C. BISCHOF, S. BLACKFORD, J. DEMMEL, J. DONGARRA, J. DU CROZ, A. GREENBAUM, S. HAMMARLING, A. MCKENNEY, and D. SORENSEN, LAPACK Users’ Guide, 3rd ed., Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, (1999); available on the Internet at www.netlib.org/lapack.
   Google Scholar
• N. HIGHAM, Accuracy and Stability of Numerical Algorithms. 2nd ed., Cambridge University Press, New York (2002).
   Google Scholar
• W. PRESS, S. TEUKOLSKY, W. VETTERLING, and B. FLANNERY, Numerical Recipes in C, 2nd ed., Cambridge University Press, New York (1996).
   Google Scholar
• M. ABRAMOWITZ and I. STEGUN, Eds., Handbook of Mathematical Functions, Dover Publications, Mineola, New York (1972).
   Google Scholar
• I. GOOD, “The Colleague Matrix, A Chebyshev Analogue of the Companion Matrix,” Q. J. Math., 12, 2, 61 (1961).
   Google Scholar
• S. BARNETT, “A Companion Matrix Analogue for Orthogonal Polynomials,” Linear Algebra and Its Applications, 12, 197 (1975).
   Web of Science ®Google Scholar
• E. INÖNÜ, “Orthogonality of a Set of Polynomials Encountered in Neutron-Transport and Radiative-Transfer Theories,” J. Math. Phys., 11, 2, 568 (1970).
   Web of Science ®Google Scholar
• G. SZEGÖ, Orthogonal Polynomials, Vol. 23 of Colloquium Publications, 2nd ed., American Mathematical Society, Providence, Rhode Island (1959).
   Google Scholar
• G. VAN DEN EYNDE, R. BEAUWENS, and E. MUND, “Calculating the Discrete Spectrum of the Transport Operator with Arbitrary Order Anisotropic Scattering,” Transp. Theory Stat. Phys. (accepted for publication).
   Google Scholar
• C. SIEWERT, “On Computing Eigenvalues in Radiative Transfer,” J. Math. Phys., 21, 9, 2468 (1980).
   Web of Science ®Google Scholar
• R. GARCIA and C. SIEWERT, “Benchmark Results in Radiative Transfer,” Transp. Theory Stat. Phys., 14, 4, 437 (1985).
   Google Scholar
• R. GARCIA and C. SIEWERT, “On Discrete Spectrum Calculations in Radiative Transfer,” J. Quant. Spectrosc. Radiat. Transfer, 42, 5, 385 (1989).
   Web of Science ®Google Scholar
• T. OOURA and M. MORI, “The Double Exponential Formula for Oscillatory Functions over the Half Infinite Interval,” J Comput. Appl. Math., 38, 353 (1991).
   Web of Science ®Google Scholar
• R. PIESSENS, E. DE DONCKER KAPENGA, C. UBERHUBER, and D. KAHANER, Quadpack: A Subroutine Package for Automatic Integration (Springer Series in Computational Mathematics), Springer-Verlag, Berlin (1983).
   Google Scholar
• M. IRI, S. MORIGUTI, and Y. TAKASAWA, “On a Certain Quadrature Formula,” J. Comput. Appl. Math., 17, 3 (1987) (translation of the original Japanese paper published in 1970).
   Web of Science ®Google Scholar
• A. ABDALLAH, “Calculation of the Thermal Disadvantage Factor in a Heterogeneous Slab Cell,” Nucl. Sci. Eng., 101, 384 (1989).
   Web of Science ®Google Scholar
• G. BOND and C. SIEWERT, “The Effect of Linearly Anisotropic Neutron Scattering on Disadvantage Factor Calculations,” Nucl. Sci. Eng., 35, 277 (1969).
   Web of Science ®Google Scholar
• G. ECCLESTON and N. McCORMICK, “One-Speed Transport Disadvantage Factor Calculations for General Anisotropic Scattering,” J. Nucl. Energ., 24, 23 (1970).
   Web of Science ®Google Scholar
• W. REED, “New Difference Schemes for the Neutron Transport Equation,” Nucl. Sci. Eng., 46, 309 (1971).
   Web of Science ®Google Scholar
• B. GANAPOL, Personal Communication regarding BLUE (2005).
   Google Scholar
• C. BREZINSKI, Algorithmes d’accélération de la convergence. Étude numérique, Editions Technip, Paris (1978).
   Google Scholar
• L. HENYEY and J. GREENSTEIN, “Diffuse Radiation in the Galaxy,” Astrophy. J., 93, 70 (1941).
   Web of Science ®Google Scholar