Discrete High-dimensional Neutron Transport Equation Format And Parallel Algorithms

Motivated by issues from applications and requirements in the future, this paper is focused on the numerical simulations for the multi-dimensional neutron transport equation. Firstly, the "symmetry" property of the two-dimensional discrete schemes and the prior estimates of the three-dimensional discrete solutions have been studied in theory. Then, the parallel algorithms and the convergence acceleration methods have been designed and applied. Some significant results have been achieved.Eight chapters are included in this paper.The background and the development of the numerical methods for particle transport are introduced in the first chapter. The research status of USA and Russia etc. are investigated, with the emphasis on the representative achievements on the methods and codes in LANL in recent 50 years. Especially, the development of the parallel algorithms for transport problems combined with that of the parallel computers is described briefly. The domestic status, mainly being in IAPCM, is introduced. Furthermore, the work and innovation of this paper are summarized.The neutron transport equations and their discrete schemes are introduced in Chapter 2. Starting with the basic concept about particle transport and the universal form of transport equation, the discuss is concentrated upon the transport equation and the implicit difference scheme under 3-D Cartesian coordinate, as well as the transport equation and the discontinuous finite element scheme under 2-D cylindrical geometry.In Chapter 3, the prior estimates about the 3-D difference solution and its difference quotients on time space and geometry space are made by means of discrete functional analysis, so that the stability and the convergence of the 3-D difference solution are obtained.The "1-D sphere symmetry" property of the discrete schemes for the time-dependent neutron transport equation under 2-D cylindrical geometry, which is adifficult issue existing in practical applications for many years, is discussed thoroughly in Chapter 4. By the theoretical analysis, some results which can guide the applications are acquired.The domain decomposition parallel iterative algorithm for the 3-D time-dependent neutron transport difference equation is presented in Chapter 5. This algorithm is highly parallelizable and scalable. Furthermore, the implementation and the error estimates for both the serial and the parallel iteration are provided.In order to accelerate iterative convergence, the multigrid algorithm for the 3-D time-dependent neutron transport difference equation is researched in Chapter 6. The detail description for this algorithm and the steps o f the implementation are given. Combining the domain decomposition with the multigrid algorithm, the domain decomposition multigrid parallel algorithm is posed.In the 7th chapter, the numerical experiments concerned in the above serial and parallel algorithms are introduced, and the experimental results about various models as well as the analysis and comparison are given.The conclusions for the research work of this paper are surveyed in the last chapter.