报告题目：roubled-cell Indicator for Conservation Laws based on Artificial NeuraNetwork with Embedding Characteristic features

报告人：刘铁钢教授 北京航空航天大学数学科学学院

报告时间：2020年10月31日 上午10:00-11:00

报告地点：数理楼145报告厅

报告摘要：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.

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