Model Order Reduction for Problems with Large Convection Effects
Model Order Reduction for Problems with Large Convection Effects
复制标题
具有大对流效应问题的模型降阶
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
B. Stamm
中科院分区：
文献类型：
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作者：
N. Cagniart;Y. Maday;B. Stamm
减少的基础方法允许提出准确的近似许多参数依赖的偏微分方程，几乎在真实的时间，至少如果Kolmogorov n-宽度的所有解决方案的集合，根据变化的参数，是小的。这个想法是，任何解决方案都可以很好地近似于一些精心选择的解决方案的线性组合，这些解决方案是针对一些精心选择的参数值一次性离线计算的（通过另一种更昂贵的离散化）。然而，在某些情况下，例如具有大对流效应的问题，线性表示是不够的，因此，需要对解集进行变换/扭曲，使得适当的扭曲和适当的线性组合的组合恢复精确的近似。本文提出了一种简单的方法，初步模拟支持这种方法。
The reduced basis method allows to propose accurate approximations for many parameter dependent partial differential equations, almost in real time, at least if the Kolmogorov n-width of the set of all solutions, under variation of the parameters, is small. The idea is that any solutions may be well approximated by the linear combination of some well chosen solutions that are computed offline once and for all (by another, more expensive, discretization) for some well chosen parameter values. In some cases, however, such as problems with large convection effects, the linear representation is not sufficient and, as a consequence, the set of solutions needs to be transformed/twisted so that the combination of the proper twist and the appropriate linear combination recovers an accurate approximation. This paper presents a simple approach towards this direction, preliminary simulations support this approach.