Characteristic-featured troubled-cell indicator for Conservation Laws based on Artificial Neural Network
Prof. Tie-Gang Liu
Beihang University

We use exact solutions of one-dimensional Burgers equation to train an artificial neuron as a shock wave detector. The expression of the artificial neuron detector is then modified into a practical form to reflect admissible jump of eigenvalues. We show the working mechanism of the practical form is consistent with compressing or intersecting of characteristic curves. In addition, we prove there is indeed a discontinuity inside the cell detected by the practical form, and smooth extrema and large gradient regions are never marked. As a result, we apply the practical form to numerical schemes as a shock wave indicator with its easy extension to multi-dimensional conservation laws. Numerical results are present to demonstrate the robustness of the present indicator under Runge-Kutta Discontinuous Galerkin framework, its performance is generally compared to TVB-based indicators more efficiently and accurately. 

About the Speaker



曾任教育部高等教育数学专业类教学指导委员会秘书长、中国数学会理事、中国工业与应用数学学会常务理事、中国计算数学学会常务理事、北京数学学会常务理事。现任北京计算数学学会常务理事,《数值计算与计算机应用》《计算物理》等国内期刊及《Numerical MathematicsTheoryMethods and Applications》、《Advances in Applied Mathematics & Mechanics》国际SCI期刊编委。

2021-11-09 10:00 AM
Room: Tencent Meeting
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