Noise propagation in hybrid models of nonlinear systems: The Ginzburg-Landau equation
Noise propagation in hybrid models of nonlinear systems: The Ginzburg-Landau equation
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非线性系统混合模型中的噪声传播：Ginzburg-Landau 方程
DOI：
10.1016/j.jcp.2014.01.015
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
D. Tartakovsky
中科院分区：
文献类型：
--
作者：
S. Taverniers;F. Alexander;D. Tartakovsky
每一种物理现象都可以用保真度不同的多个模型来描述。高保真度模型（例如，分子动力学模拟）的计算成本总是高于低保真度模型（例如，基于微分方程的连续体模型）。虽然前者可能不适合大规模模拟，但后者并非普遍有效。混合算法在粗尺度模型的计算效率和精细尺度描述的表示精度之间提供了一种折衷。这是通过在绝对需要的子域中进行精细计算（例如，由于连续统模型的局部破坏）并将其与计算域中其余部分的粗尺度计算相结合来实现的。本文分析了由非线性混合系统的精细分量产生的随机波动对混合系统整体精度和稳定性的影响。两种随时间变化的金兹堡-朗道方程（GLE）及其离散表示由最近邻Ising模型提供作为计算试验台。我们的分析表明，在一维模拟中耦合这些描述会导致错误的结果。在GLE中加入随机源项可以准确预测感兴趣的量（磁化）的平均行为。它还允许两个GLE变体正确捕获微尺度波动的强度。我们的工作证明了精细尺度噪声在混合模拟中的重要性，并建议需要用其随机对应物取代混合模拟中其他确定性的粗尺度成分。
Every physical phenomenon can be described by multiple models with varying degrees of fidelity. The computational cost of higher fidelity models (e.g., molecular dynamics simulations) is invariably higher than that of their lower fidelity counterparts (e.g., a continuum model based on differential equations). While the former might not be suitable for large-scale simulations, the latter are not universally valid. Hybrid algorithms provide a compromise between the computational efficiency of a coarse-scale model and the representational accuracy of a fine-scale description. This is achieved by conducting a fine-scale computation in subdomains where it is absolutely required (e.g., due to a local breakdown of a continuum model) and coupling it with a coarse-scale computation in the rest of a computational domain. We analyze the effects of random fluctuations generated by the fine-scale component of a nonlinear hybrid on the hybridʼs overall accuracy and stability. Two variants of the time-dependent Ginzburg–Landau equation (GLE) and their discrete representations provided by a nearest-neighbor Ising model serve as a computational testbed. Our analysis shows that coupling these descriptions in a one-dimensional simulation leads to erroneous results. Adding a random source term to the GLE provides accurate prediction of the mean behavior of the quantity of interest (magnetization). It also allows the two GLE variants to correctly capture the strength of the microscale fluctuations. Our work demonstrates the importance of fine-scale noise in hybrid simulations, and suggests the need for replacing an otherwise deterministic coarse-scale component of the hybrid with its stochastic counterpart.
影响因子：
4.7
作者：
Boso, Francesca;Battiato, Ilenia
通讯作者：
Battiato, Ilenia