SIMULATION OF COMPLEX DYNAMICS USING POD 'ON THE FLY' AND RESIDUAL ESTIMATES
SIMULATION OF COMPLEX DYNAMICS USING POD 'ON THE FLY' AND RESIDUAL ESTIMATES
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DOI：
10.3934/proc.2015.1060
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发表时间：
2015-11
期刊：
影响因子：
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通讯作者：
F. Terragni;J. Vega
中科院分区：
文献类型：
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作者：
F. Terragni;J. Vega
本征正交分解（POD）是一种非常有效的方法，可以用来识别包含在包含耗散偏微分方程组数值计算轨迹的快照集合中的动力学信息。这些信息被组织在POD模式的层次结构中，并且系统可以被Galerkin投影到相关联的线性子空间上。通常，结果是问题的低维模型。如果POD被应用“在飞行中”，自适应地结合标准的数值求解器（它提供必要的快照）与减少的系统在穿插的间隔，作为时间和分叉参数的变化，可以提高灵活性和效率的近似。残差估计的引入，使这种适应准确和强大的，防止可能的模式截断不稳定性，在复杂的动态。所有的想法都说明了一些分歧的情况下，包括准周期和混沌吸引子，这突出了一个良好的计算效率。
Proper orthogonal decomposition (POD) is a very effective means to identify dynamical information contained in sets of snapshots that cover numerically computed trajectories of dissipative systems of partial differential equations. Such information is organized in a hierarchy of POD modes and the system can be Galerkin-projected onto the associated linear subspace. Quite frequently, the outcome is a low dimensional model of the problem. Flexibility and efficiency of the approximation can be enhanced if POD is applied `on the fly', adaptively combining a standard numerical solver (which provides the necessary snapshots) with the reduced system in interspersed intervals, as both time and a bifurcation parameter are varied. Residual estimates are introduced to make this adaptation accurate and robust, preventing possible mode truncation instabilities in the presence of complex dynamics. All ideas are illustrated in some bifurcation scenarios including quasi-periodic and chaotic attractors, which highlights a good computational efficiency.