摘要：In this talk, we present sparse grid discontinuous Galerkin (DG) schemes for solving high-dimensional PDEs. The scheme is constructed based on the standard weak form of the DG method and sparse grid finite element spaces built from multiwavelets. The interpolatory multiwavelets are introduced to efficiently deal with the nonlinear terms. This scheme is demonstrated to be effective in adaptive calculations, particularly for high dimensional applications. Numerical results for Hamilton-Jacobi equations, nonlinear Schrodinger equations and wave equations will be discussed.

报告人简介：Dr. Juntao Huang is an Assistant Professor at Texas Tech University. He obtained the Ph.D. degree in Applied Math in 2018 and the bachelor degree in 2013 from Tsinghua University. Prior to joining Texas Tech University in 2022, he worked as a visiting assistant professor at Michigan State University. His research interests involve the design and analysis of high-order numerical methods for PDEs and using machine learning to assist traditional scientific computing tasks. His recent work includes structure-preserving machine learning moment closures for kinetic models and adaptive sparse grid discontinuous Galerkin (DG) methods for high-dimensional PDEs.