Title: Sparse grid discontinuous Galerkin (DG) methods for high dimensional PDEs 

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Abstract: In this talk, I will introduce adaptive sparse grid DG methods, and discuss their applications in solving high dimensional PDEs, including kinetic equations, Hamilton-Jacobi equations, etc. The methods, which combines the advantages of sparse grid and DG approach, are shown to be particularly effective for high dimensional transport equations.The methods are constructed using multiwavelets of various kinds. We prove stability and accuracy for model equations. Adaptivity is incorporated for time evolution problems. Benchmark test results are shown.

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Biography: Yingda Cheng is currently professor of mathematics and an affiliate faculty with computational modeling & data analytics program at Virginia Polytechnic Institute and State University (Virginia Tech). She was born in Hefei, China in 1983 and received her B.S. degree from the University of Science and Technology of China in 2003. She graduated with a Ph.D. degree in applied mathematics from Brown University in 2007. After a postdoctoral position at the University of Texas at Austin, Dr. Cheng was a faculty member at Michigan State University before the recent move to Virginia Tech.

Dr. Cheng's area of research is in scientific computing, numerical analysis, applied mathematics and data-driven modeling and computation, with applications in plasma physics, semiconductor devices, fluid mechanics, etc. She is interested in developing numerical schemes for PDEs governing complex physical behaviors in science and engineering. She has worked extensively on the construction and analysis of discontinuous Galerkin schemes and structure-preserving numerical schemes that tackles the curse of dimensionality for kinetic transport equations.