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Some new perspectives on developing asymptotic preserving schemes

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FKTW05 - Frontiers in numerical analysis of kinetic equations

In this talk, I will introduce two new approaches for constructing asymptotic preserving schemes for kinetic equations using variational formulations. One invokes the power of neural networks, and we show uniform stability in the sense that the numerical error can be controlled by the loss function of the neural networks. The other is based on a minimizing movement scheme, which takes the advantage of the versatile optimization toolbox. In this case, we discuss the uniform convergence rate with respect to the scaling parameters. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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