Reconstruction of a velocity field for a 3-D advection–diffusion equation
Reconstruction of a velocity field for a 3-D advection–diffusion equation
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DOI：
10.1016/j.ijthermalsci.2011.08.002
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发表时间：
2011-12
影响因子：
4.5
通讯作者：
Yixin Dou;B. Han
中科院分区：
文献类型：
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作者：
Yixin Dou;B. Han
本文研究三维对流扩散方程的分段常速场的重建问题。重建速度场对于认识造山带地形的形成和演化具有重要意义。为了抑制测量误差和识别尖锐的特征，我们提出了一种新的正则化集成l1数据保真度与总变差1惩罚项重建分段恒定速度场。为了测试我们提出的正则化方法的性能，我们比较了四种不同的正则化方法。通过数值实验，我们可以得出结论：（1）l1数据保真度可以抑制包括高斯噪声和非高斯噪声在内的测量误差;（2）总变差惩罚项具有识别尖锐特征的能力。
This work deals with the reconstruction of a piecewise constant velocity field for a 3-D advection–diffusion equation. Reconstructing a velocity field often plays an important role in understanding the formation and evolution of orogenic topography. In order to suppress measurement errors and to identify sharp features, we propose a new regularization integrating an l1data fidelity with a total variation1penalty term to reconstruct a piecewise constant velocity field. For testing the performance of our proposed regularization method, we compare four different regularization methods. From numerical experiments, we can draw conclusions: (I) an l1data fidelity can suppress measurement errors including Gaussian noise and non-Gaussian noise; (II) a total variation penalty term has the ability to identify sharp features.