Abstract Proper generalized decomposition (PGD) can be described as a numerical extension of separation of variables and thus be employed as a solution technique for multi-dimensional problems, where dimensions should be understood in the phase-space context of the governing law at hand. This paper presents a PGD approach on efficiently solving problems involving multigroup neutron diffusion. Two PGD approaches are described: space-only and space-energy decompositions. Numerical results include 2-D and 3-D examples with two-, seven-, and 145-group structures. The PGD solutions are compared against traditional multi-dimensional finite element discretization. For few-group problems, both PGD approaches prove effective for mildly heterogeneous geometries, but showed reduced performance with increasing heterogeneity. The space-energy representation was found to be slower than the space-only approach for two-group problems, but proved more effective for seven-group problems. For even larger numbers of groups, the space-energy PGD decomposition was very effective at reducing the computational time.

中文翻译：

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使用适当广义分解的多群中子扩散的空间能量分离表示

摘要 适当的广义分解 (PGD) 可以被描述为变量分离的数值扩展，因此可用作多维问题的解决技术，其中维度应该在手头的控制法则的相空间上下文中理解。本文提出了一种有效解决涉及多群中子扩散问题的 PGD 方法。描述了两种 PGD 方法：仅空间分解和空间能量分解。数值结果包括具有二组、七组和 145 组结构的 2-D 和 3-D 示例。PGD​​ 解决方案与传统的多维有限元离散化进行了比较。对于少组问题，两种 PGD 方法都证明对轻度异质几何结构有效，但随着异质性的增加，性能会降低。发现空间能量表示对于两组问题比仅空间方法慢，但被证明对七组问题更有效。对于更多的组，空间能量 PGD 分解在减少计算时间方面非常有效。