I investigate the suitability of the Scheduled-Relaxation-Jacobi method as a smoother within a geometric multilevel (ML) solver. Its performance in the solution of a linear elliptic equation is measured, based on two metrics: absolute performance (measured by the residual reduction in a fixed number of iterations), and parallel scalability. I discuss the theoretical expectations on the effect of this hybrid scheme on the solution iterate and, especially, the solution error, and confirm them numerically.

中文翻译：

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几何多级设置中计划松弛Jacobi方法的性能。一，线性情况

我研究了Scheduled-Relaxation-Jacobi方法是否适合作为几何多级（ML）求解器中的平滑器。基于两个指标来测量其在线性椭圆方程解中的性能：绝对性能（通过固定迭代次数的残差减少量测量）和并行可伸缩性。我讨论了关于此混合方案对解决方案迭代（尤其是解决方案误差）影响的理论期望，并进行了数值验证。