A new approach to proper orthogonal decomposition with difference quotients
A new approach to proper orthogonal decomposition with difference quotients
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DOI：
10.1007/s10444-023-10011-9
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发表时间：
2021-06
影响因子：
1.7
通讯作者：
Sarah Locke Eskew;J. Singler
中科院分区：
文献类型：
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作者：
Sarah Locke Eskew;J. Singler
在最近的工作中（Koc等人，SIAM J.编号Anal.59（4），2163-2196，），作者表明，包括差异系数（DQ）是必要的，以证明最佳逐点的时间误差界的适当正交分解（POD）降阶模型的热方程。在这项工作中，我们介绍了一种新的方法，包括DQ的POD过程。代替使用所有快照数据和DQ来计算POD模式，我们仅使用第一快照沿着所有DQ和特殊POD权重。我们表明，这种方法保留了标准POD DQ方法的所有数值分析优势，同时使用的POD数据集的快照数量约为标准POD DQ方法的一半，即，新方法需要较少的计算工作量。我们用数值实验来说明我们的理论结果。
In a recent work (Koc et al., SIAM J. Numer. Anal.59(4), 2163–2196, ), the authors showed that including difference quotients (DQs) is necessary in order to prove optimal pointwise in time error bounds for proper orthogonal decomposition (POD) reduced order models of the heat equation. In this work, we introduce a new approach to including DQs in the POD procedure. Instead of computing the POD modes using all of the snapshot data and DQs, we only use the first snapshot along with all of the DQs and special POD weights. We show that this approach retains all of the numerical analysis benefits of the standard POD DQ approach, while using a POD data set that has approximately half the number of snapshots as the standard POD DQ approach, i.e., the new approach requires less computational effort. We illustrate our theoretical results with numerical experiments.