TY - JOUR
T1 - An adaptive sparse grid local discontinuous Galerkin method for Hamilton-Jacobi equations in high dimensions
AU - Guo, Wei
AU - Huang, Juntao
AU - Tao, Zhanjing
AU - Cheng, Yingda
N1 - Funding Information:
We would like to thank Qi Tang and Kai Huang for the assistance and discussion in code implementation. Yingda Cheng would like to thank the support from IPAM to attend the workshop on “High-dimensional Hamilton-Jacobi PDEs”.
Funding Information:
Research is supported by NSF grant DMS-1830838.Research is supported by NSFC Grant 12001231.Research is supported by NSF grants DMS-1453661 and DMS-1720023.We would like to thank Qi Tang and Kai Huang for the assistance and discussion in code implementation. Yingda Cheng would like to thank the support from IPAM to attend the workshop on ?High-dimensional Hamilton-Jacobi PDEs?.
Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/7/1
Y1 - 2021/7/1
N2 - The Hamilton-Jacobi (HJ) equations arise in optimal control and many other applications. Oftentimes, such equations are posed in high dimensions, and this presents great numerical challenges. In this paper, we propose an adaptive sparse grid (also called adaptive multiresolution) local discontinuous Galerkin (DG) method for solving Hamilton-Jacobi equations in high dimensions. By using the sparse grid techniques, we can treat moderately high dimensional cases. Adaptivity is incorporated to capture kinks and other local structures of the solutions. Two classes of multiwavelets including the orthonormal Alpert's multiwavelets and the interpolatory multiwavelets are used to achieve multiresolution. Numerical tests in up to four dimensions are provided to validate the performance of the method.
AB - The Hamilton-Jacobi (HJ) equations arise in optimal control and many other applications. Oftentimes, such equations are posed in high dimensions, and this presents great numerical challenges. In this paper, we propose an adaptive sparse grid (also called adaptive multiresolution) local discontinuous Galerkin (DG) method for solving Hamilton-Jacobi equations in high dimensions. By using the sparse grid techniques, we can treat moderately high dimensional cases. Adaptivity is incorporated to capture kinks and other local structures of the solutions. Two classes of multiwavelets including the orthonormal Alpert's multiwavelets and the interpolatory multiwavelets are used to achieve multiresolution. Numerical tests in up to four dimensions are provided to validate the performance of the method.
KW - Adaptivity
KW - Hamilton-Jacobi equations
KW - High dimensions
KW - Local discontinuous Galerkin
KW - Sparse grid
UR - http://www.scopus.com/inward/record.url?scp=85103323752&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2021.110294
DO - 10.1016/j.jcp.2021.110294
M3 - Article
AN - SCOPUS:85103323752
VL - 436
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
M1 - 110294
ER -