A Fast Multigrid Algorithm for Isotropic Transport Problems I: Pure Scattering
A Fast Multigrid Algorithm for Isotropic Transport Problems I: Pure Scattering
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一种求解各向同性传输问题的快速多重网格算法 I：纯散射
DOI：
10.1137/0916038
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
G. Yang
中科院分区：
文献类型：
--
作者：
T. Manteuffel;S. McCormick;J. Morel;S. Oliveira;G. Yang
本文提出了一种求解一维板状方程组的多重网格方法。该方案与大规模并行计算机体系结构高度兼容，并代表了曲线和多维几何中$S_N $方程的类似多重网格方法的第一步。对我们的方案进行了广泛的理论分析，表明它是非常有效的。事实上，该方法是如此有效，它几乎代表了一个精确的解决方案的技术。计算结果验证了理论分析的正确性。吸收的情况在本文的续集中处理[Manteuillet et al.，一个快速多重网格算法输运问题II：吸收，SIAM J。计算：提交]。
The authors present a multigrid method for solving the one-dimensional (1-D) slab-geometry $S_N $ equations with isotropic scattering and no absorption. This scheme is highly compatible with massively parallel computer architectures and represents a first step toward similar multigrid methods for the $S_N $ equations in curvilinear and multidimensional geometries. Extensive theoretical analyses are given for our scheme which indicate that it is extremely efficient. In fact, the method is so efficient that it very nearly represents an exact solution technique. Results from calculations are presented which validate the theoretical results. The case with absorption is treated in a sequel to this paper [Manteuffel et al., A fast multigrid algorithm for transport problems II: With absorption, SIAM J. Sci. Comput., submitted].