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Model Reduction for Transport-Dominated Problems via Online Adaptive Bases and Adaptive Sampling
SIAM Journal on Scientific Computing ( IF 3.0 ) Pub Date : 2020-09-21 , DOI: 10.1137/19m1257275
Benjamin Peherstorfer

SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page A2803-A2836, January 2020.
This work presents a model reduction approach for problems with coherent structures that propagate over time, such as convection-dominated flows and wave-type phenomena. Traditional model reduction methods have difficulties with these transport-dominated problems because propagating coherent structures typically introduce high-dimensional features that require high-dimensional approximation spaces. The approach proposed in this work exploits the locality in space and time of propagating coherent structures to derive efficient reduced models. Full-model solutions are approximated locally in time via local reduced spaces that are adapted with basis updates during time stepping. The basis updates are derived from querying the full model at a few selected spatial coordinates. A core contribution of this work is an adaptive sampling scheme for selecting at which components to query the full model to compute basis updates. The presented analysis shows that, in probability, the more local the coherent structure is in space, the fewer full-model samples are required to adapt the reduced basis with the proposed adaptive sampling scheme. Numerical results on benchmark examples with interacting wave-type structures and time-varying transport speeds and on a model combustor of a single-element rocket engine demonstrate the wide applicability of the proposed approach and runtime speedups of up to one order of magnitude compared to full models and traditional reduced models.


中文翻译:

通过在线自适应基和自适应采样对运输主导问题进行模型简化

SIAM科学计算杂志,第42卷,第5期,第A2803-A2836页,2020年1月。
这项工作为相干结构随时间传播的问题(例如对流主导的流动和波浪型现象)提出了一种模型简化方法。传统的模型简化方法难以解决这些以运输为主导的问题,因为传播的相干结构通常会引入需要高维近似空间的高维特征。这项工作中提出的方法利用了传播相干结构的空间和时间局部性,以得出有效的简化模型。全模型解决方案通过局部缩减的空间在时间上进行本地近似,该局部缩减的空间在时间步长过程中根据基础更新进行调整。基础更新是通过在几个选定的空间坐标处查询完整模型得出的。这项工作的核心贡献是一种自适应采样方案,用于选择在哪个组件上查询完整模型以计算基础更新。所提出的分析表明,在可能性上,相干结构在空间中的局部性越强,则使用提出的自适应采样方案来适应缩减基数所需的全模型样本就越少。在具有交互波型结构和时变运输速度的基准示例上以及在单元素火箭发动机的模型燃烧器上的数值结果表明,所提出的方法具有广泛的适用性,与完全运行相比,运行时间提速高达一个数量级。模型和传统简化模型。相干结构在空间中的局部性越强,所需的全模型样本就越少,以利用提出的自适应采样方案来适应简化后的基础。在具有交互波型结构和时变运输速度的基准示例上以及在单元素火箭发动机的模型燃烧器上的数值结果表明,所提出的方法具有广泛的适用性,与完全运行相比,运行时间提速高达一个数量级。模型和传统简化模型。相干结构在空间中的局部性越强,所需的全模型样本就越少,以利用提出的自适应采样方案来适应简化后的基础。在具有交互波型结构和时变运输速度的基准示例上以及在单元素火箭发动机的模型燃烧器上的数值结果表明,所提出的方法具有广泛的适用性,与完全运行相比,运行时间提速高达一个数量级。模型和传统简化模型。
更新日期:2020-10-16
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