Bi-directional coupling between a PDE-domain and an adjacent Data-domain equipped with multi-fidelity sensors
Bi-directional coupling between a PDE-domain and an adjacent Data-domain equipped with multi-fidelity sensors
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DOI：
10.1016/j.jcp.2018.07.039
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发表时间：
2018-12
期刊：
影响因子：
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通讯作者：
Dongkun Zhang;Liu Yang;G. Karniadakis
中科院分区：
文献类型：
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作者：
Dongkun Zhang;Liu Yang;G. Karniadakis
我们考虑一个新的原型问题，在区域分解的解决方案，在一个域由一个已知的偏微分方程（PDE），而在相邻的域的解决方案是重建从分布式传感器（数据）的可变保真度收集的信息。PDE域和数据域是紧密耦合的，因为PDE解决方案由收集的数据驱动，而从其相关传感器收集的信息受PDE解决方案的影响。我们的整体方法是基于施瓦茨交替方法和高斯过程回归（GPR）的最新进展，使用多保真度数据。以一维和二维Helmholtz方程为例，验证了所提区域分解算法的有效性.
We consider a new prototype problem in domain decomposition with the solution in one domain governed by a known partial differential equation (PDE) whereas the solution in an adjacent domain is reconstructed by information gathered from distributed sensors (data) of variable fidelity. The PDE-domain and the Data-domain are tightly coupled, as the PDE solution is driven by the collected data, while the information gathered from its associated sensors is influenced by the PDE solution. Our overall methodology is based on the Schwarz alternating method and on recent advances in Gaussian process regression (GPR) using multi-fidelity data. The effectiveness of the proposed domain decomposition algorithm is demonstrated by examples of Helmholtz equations in both one-dimensional (1D) and two-dimensional (2D) domains.