References
- Ackroyd , R. T. 1983 . Least‐squares derivation of extremum and weighted‐residual methods for equations of reactor physics . Ann. Nucl. Energy , 10 : 65 – 99 .
- Ackroyd , R. T. 1986 . Generalized least squares as a generator of variational principles and weighted residual methods for fem transport methods . Prog. Nucl. Energy , 18 ( 1/2 ) : 45 – 62 . [CROSSREF]
- Agoshkov , V. 1998 . “ Boundary value problems for transport equations ” . In Modeling and Simulation in Science, Engineering and Technology Birkhäuser .
- Borysiewicz , M. and Stankiewicz , R. 1979a . Weak solution and approximate methods for the transport equation . J. Math. Anal. Appl. , 68 : 191 – 210 . [CROSSREF]
- Borysiewicz , M. and Stankiewicz , R. 1979b . Variational formulation and projectional methods for the second order transport equation . J. Math. Anal. Appl. , 71 : 210 – 231 . [CROSSREF]
- Brown , P. N. , Lee , B. and Manteuffel , T. A. 2003 . A moment‐parity multigrid preconditioner for the first‐order system least‐squares formulation of the Boltzmann transport equation . SIAM J. Numer. Anal. , 25 ( 2 ) : 513 – 533 .
- Cercignani , C. 1969 . Mathematical Methods in Kinetic Theory New York : Plenum Publishing Company .
- Cessenat , M. 1984 . Théorèmes de trace pour des espaces de fonctions de la neutronique . C.R. Acad. Sci. Paris , 16 ( Sér I ) : 831 – 834 .
- Cessenat , M. 1985 . Théorèmes de trace pour des espaces de fonctions de la neutronique . C.R. Acad. Sci. Paris , 3 ( Sér. I ) : 89 – 92 .
- Chang , B. and Lee , B. 2003 . A multigrid algorithm for solving the multigroup, anisotropic scattering Boltzmann equation using first‐order system least‐squares methodology . ETNA , 15 : 132 – 151 .
- Chang , B. and Lee , B. “ Space‐angle first‐order system least‐squares (FOSLS) for the linear Boltzmann equation ” . Lawrence Livermore National Laboratory, Center for Applied Scientific Computing . preprint
- Dautray , R. and Lions , J. L. 1985 . Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques Masson .
- Duderstadt , J. J. and Martin , W. R. 1979 . Transport Theory John Wiley & Sons .
- Greenberg , W. , Der Mee , C. V. and Protopopescu , V. 1987 . Boundary Value Problems in Abstract Kinetic Theory Birkhäuser Verlag .
- Kaper , H. G. , Lekkerkerker , C. G. and Hejtmanek , J. 1982 . Spectral Methods in Linear Transport Theory Birkhäuser Verlag .
- Manteuffel , T. A. and Ressel , K. 1998 . Least‐squares finite‐element solution of the neutron transport equation in diffusive regimes . SIAM J. Numer. Anal. , 35 ( 2 ) : 806 – 853 . [CROSSREF]
- Manteuffel , T. A. , Ressel , K. and Starke , G. 2000 . A boundary functional for the least‐squares finite‐element solution of the neutron transport equation . SIAM J. Numer. Anal. , 37 ( 2 ) : 556 – 586 . [CROSSREF]
- Martin , W. R. and Duderstadt , J. J. 1977 . Finite element solutions of the neutron transport equation with applications to strong heterogeneities . Nucl. Sci. Eng. , 62 : 371 – 390 .
- Mokhtar‐Karroubi , M. 1997 . Mathematical Topics in Neutron Transport Theory , Series on Advances in Mathematics for Applied Sciences Vol. 46 , Word Scientific .
- Morel , J. E. and McGhee , J. M. 1999 . A self‐adjoint angular flux equation . Nucl. Sci. Eng. , 132 : 312 – 325 .
- Pitkaranta , J. 1975 . A non‐self‐adjoint variational procedure for the finite‐element approximation of the transport equation . Trans. Theory Statist. Phys. , 4 ( 1 ) : 1 – 24 .
- Pitkaranta , J. 1976 . On the variational approximation of the transport operator . J. Math. Anal. Appl. , 54 : 419 – 440 . [CROSSREF]
- Planchard , J. 1995 . Méthodes Mathématiques en Neutronique Eyrolles .
- Pomraning , G. C. and Clark , M. Jr. 1963 . The variational method applied to the monoenergetic Boltzmann equation, Part II . Nucl. Sci. Eng. , 16 : 155 – 164 .
- Raviart , P. A. and Thomas , J. M. 1992 . Introduction à l'Analyse Numérique des Équations aux Dérivées Partielles Masson .
- Ukaï , S. 1972 . Solution of the multidimensional neutron transport equation by finite element methods . J. Nucl. Sci. Technol. , 9 ( 6 ) : 366 – 373 .
- Vladimirov , V. S. 1963 . Mathematical Problems in the One‐Velocity Theory of Particles Transport Vol. 61 , 1961 Ontario : Atomic Energy of Canada Ltd . translated from Trans. V.A. Steklov Mathematical Institute