Abstract:

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 and is free of curse of dimensionality. 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.

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 both from Tsinghua University. Prior to joining Texas Tech University in 2022, he worked as a visiting assistant professor at Michigan State University. His current research interests focus on the design and analysis of numerical methods for PDEs and using machine learning to assist traditional scientific computing tasks. His research has been supported by National Science Foundation and Office of Naval Research in the United States. He has published 30+ papers in top journals including Journal of Computational Physics, Journal of Scientific Computing, SIAM Journal on Scientific Computing, SIAM Multiscale Modeling and Simulation, and Mathematics of Computation.