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首页> 外文期刊>Japan journal of industrial and applied mathematics >The danger of combining block red-black ordering with modified incomplete factorizations and its remedy by perturbation or relaxation
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The danger of combining block red-black ordering with modified incomplete factorizations and its remedy by perturbation or relaxation

机译：通过扰动或放松将块红黑色排序组合红黑排序的危险及其补救措施

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摘要

Modified incomplete LU/Cholesky factorizations without fill-ins are popular preconditioners for Krylov subspace methods, because they require no extra memory and have more potential of accelerating the convergence than simple ILU/IC preconditioners. For parallelizing preconditioners, the block red-black ordering is attractive due to its highly parallel nature and small number of synchronization points. Hence, their combination seems to produce powerful and parallelizable preconditioners. In fact, however, this combination can cause breakdown of the factorization due to the occurrence of zero pivots. We analyze this phenomenon and give necessary and sufficient conditions of zero pivots in the case of a regular grid. We also show both theoretically and experimentally that adding perturbation to the diagonal elements or relaxing the compensation of dropped fill-ins is useful to alleviate the problem. Numerical tests show that the resulting preconditioners are highly effective and are applicable for up to 10(-3) level of parallelism.
机译：没有填充的修改不完整的LU / Cholesky InsionIzations是Krylov子空间方法的流行预处理器，因为它们不需要额外的内存，并且具有比简单的ILU / IC预处理程序更快地加速收敛的潜力。对于并行化预处理器，由于其高度平行的性质和少量同步点，块红黑色排序具有吸引力。因此，它们的组合似乎产生了强大而平行的前提者。然而，事实上，由于零枢轴的发生，这种组合可能导致因分解的分解。我们分析了这种现象，在常规网格的情况下给出了必要和充分的零枢轴条件。理论上和实验表明，在对角线元件中添加扰动或放松掉落的填充补偿的扰动是有用的，可用于缓解问题。数值测试表明，所得的预处理器具有高效，适用于高达10（-3）水平的平行度。

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