Paper Info
Title
An Adaptive Multiresolution Discontinuous Galerkin Method for Time-Dependent Transport Equations in Multidimensions.
Abstract
In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme for time-dependent transport equations in multidimensions. The method is constructed using multiwavlelets on tensorized nested grids. Adaptivity is realized by error thresholding based on the hierarchical surplus, and the Runge-Kutta DG scheme is employed as the reference time evolution algorithm. We show that the scheme performs similarly to a sparse grid DG method when the solution is smooth, reducing computational cost in multidimensions. When the solution is no longer smooth, the adaptive algorithm can automatically capture fine local structures. The method is therefore very suitable for deterministic kinetic simulations. Numerical results including several benchmark tests, the Vlasov Poisson (VP), and oscillatory VP systems are provided.
Year
DOI
Venue
2017
10.1137/16M1083190
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
Field
DocType
discontinuous Galerkin methods,adaptive multiresolution analysis,sparse grids,transport equations,Vlasov Poisson system
Discontinuous Galerkin method,Applied mathematics,Mathematical optimization,Galerkin method,Time evolution,Thresholding,Adaptive algorithm,Sparse grid,Mathematics
Journal
Volume
Issue
ISSN
39
6
1064-8275
Citations 
PageRank 
References 
2
0.39
0
Authors
2
Name
Order
Citations
PageRank
Wei Guo1505.96
Yingda Cheng220120.27