Characteristic-featured troubled-cell indicator for Conservation Laws based on Artificial Neural Network

：刘铁钢教授
：2021-01-08 14:45
：厦大海韵园实验楼105报告厅

报告人：刘铁钢（北京航空航天大学）

时  间：1月8日14:45

地  点：厦大海韵园实验楼105报告厅

内容摘要:

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.

个人简介：

刘铁钢，教授，博士生导师，北航研究生院副院长兼培养处处长，研究偏微分方程理论和偏微分方程数值解在科学与工程计算领域中的应用。在流场高精度数值方法、多介质流算法、气动优化等领域拥有前沿的研究成果。在SIAM JSC、JCP等一流期刊发表论文百余篇。曾任中国工业与应用数学会常务理事、中国计算数学学会常务理事。现任北京市计算数学学会常务理事，《Numerical Mathematics：Theory，Methods and Applications》、《Advances in Applied Mathematics & Mechanics》等多个期刊编委。

 

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