Abstract Conventionally, tens to hundreds times of repeated characteristic sweeping is required for the Method of Characteristics (MOC) to converge within the inner-outer iteration scheme, even with the acceleration techniques like CMFD and CMR employed to improve the convergence rate. Therefore, the Matrix MOC, which converts the characteristic sweeping into a linear system, was proposed attempting to accelerate the characteristic sweeping itself. However, it is computationally intensive if not prohibitive to construct and store the coefficient matrices in the explicit form. This study proposes four principle numerical properties of the coefficient matrices in the Matrix MOC. Exploiting these properties reduces significantly the memory consumption and the computational time, making it possible to explicitly store the sparse coefficient matrices in CSR (Compressed Sparse Row) scheme for large problems. The multi-group coupling GMRES (Generalized Minimal RESidual) solver is then employed to solve the Matrix MOC equations of all groups simultaneously. Since the matrices are stored explicitly in CSR scheme, the operations involving sparse matrices and vectors are performed by taking advantage of the fully optimized Intel® MKL library. The Matrix MOC based 2D code named TIGER is developed, and verified by the BWR lattice benchmark and several variations of the C5G7 problem. Numerical results demonstrate that the Matrix MOC with the proposed numerical properties has adequate accuracy, and is feasible to solve a 2D small core problem on an ordinary PC with explicitly stored matrices. In addition, the optimal parameters of the multi-group coupling GMRES solver are investigated by sensitivity analysis to get the highest computational efficiency.

中文翻译：

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矩阵MOC：矩阵形式的特征方法

摘要 传统上，即使采用CMFD和CMR等加速技术来提高收敛速度，特征方法（MOC）在内外迭代方案内收敛仍需要数十至数百次重复特征扫描。因此，提出了将特征扫描转换为线性系统的矩阵 MOC，试图加速特征扫描本身。然而，以显式形式构造和存储系数矩阵即使不是禁止的，也是计算密集型的。本研究提出了矩阵 MOC 中系数矩阵的四个主要数值特性。利用这些特性可以显着减少内存消耗和计算时间，使得在 CSR（压缩稀疏行）方案中显式存储稀疏系数矩阵成为可能，以解决大问题。然后采用多组耦合GMRES（广义最小RESidual）求解器同时求解所有组的矩阵MOC方程。由于矩阵显式存储在 CSR 方案中，因此利用完全优化的英特尔® MKL 库执行涉及稀疏矩阵和向量的操作。开发了基于矩阵 MOC 的二维代码 TIGER，并通过 BWR 点阵基准测试和 C5G7 问题的几个变体进行验证。数值结果表明，具有所提出数值特性的矩阵 MOC 具有足够的精度，并且可以在具有显式存储矩阵的普通 PC 上解决 2D 小核心问题。此外，