The growing discrepancy between CPU computing power and memory bandwidth drives more and more numerical algorithms into a bandwidth-bound regime. One example is the overlapping Schwarz smoother, a highly effective building block for iterative multigrid solution of elliptic equations with higher order finite elements. Two options of reducing the required memory bandwidth are sparsity exploiting storage layouts and representing matrix entries with reduced precision in floating point or fixed point format. We investigate the impact of several options on storage demand and contraction rate, both analytically in the context of subspace correction methods and numerically at an example of solid mechanics. Both perspectives agree on the favourite scheme: fixed point representation of Cholesky factors in nested dissection storage.

中文翻译：

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混合精度和存储布局对加性 Schwarz 平滑器的影响

CPU 计算能力和内存带宽之间越来越大的差异促使越来越多的数值算法进入带宽受限机制。一个例子是重叠 Schwarz 平滑器，这是一种高效的构建块，用于对具有高阶有限元的椭圆方程进行迭代多重网格求解。减少所需内存带宽的两个选项是稀疏性利用存储布局和以浮点或定点格式表示精度降低的矩阵条目。我们研究了几种选项对存储需求和收缩率的影响，无论是在子空间校正方法的背景下进行分析，还是在固体力学示例中进行数值分析。两种观点都同意最喜欢的方案：嵌套解剖存储中 Cholesky 因子的定点表示。