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首页> 美国政府科技报告 >THE FINITE ELEMENT METHOD FOR NEUTRON TRANSPORT PART Ⅳ A VARIATIONAL PRINCIPLE GIVING AN UPPER ROUND FOR THE LOWEST EIGENVALUE OF THE BOLTZMANN EQUATION
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THE FINITE ELEMENT METHOD FOR NEUTRON TRANSPORT PART Ⅳ A VARIATIONAL PRINCIPLE GIVING AN UPPER ROUND FOR THE LOWEST EIGENVALUE OF THE BOLTZMANN EQUATION

机译：中子输运的有限元法ⅣBoltzmann方程最低特征值的上变量原理

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A maximum principle for neutron transport in systems with extraneous sources is used with the method of source iteration to suggest a functional for a variational principle for self-sustaining systems. By using the general properties of the leakage and removal operators of the even-parity transport equation the variational principle is shown to give an upper bound to the lowest eigenvalue of the one-speed Boltzmann equation. Thus by making use of the method of Part III for a lower bound, the lowest eigenvalue can be bracketed. The variational principle leads to the finite element equations identical to those arising in the Williams/Galliara finite element formulation of the source-iteration methods, thus showing that the latter method always gives an upper bound to the lowest eigenvalue. Their upper bounds are very close to the exact value for some benchmark calculations. (ERA citation 04:030129)

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