@Article{CiCP-17-1320,
author = {Andreas Hiltebrand and Siddhartha Mishra},
title = {Efficient Preconditioners for a Shock Capturing Space-Time Discontinuous Galerkin Method for Systems of Conservation Laws},
journal = {Communications in Computational Physics},
year = {2018},
volume = {17},
number = {5},
pages = {1320--1359},
abstract = {<p style="text-align: justify;">An entropy stable fully discrete shock capturing space-time Discontinuous
Galerkin (DG) method was proposed in a recent paper [20] to approximate hyperbolic
systems of conservation laws. This numerical scheme involves the solution of a
very large nonlinear system of algebraic equations, by a Newton-Krylov method, at
every time step. In this paper, we design efficient preconditioners for the large, nonsymmetric
linear system, that needs to be solved at every Newton step. Two sets of
preconditioners, one of the block Jacobi and another of the block Gauss-Seidel type are
designed. Fourier analysis of the preconditioners reveals their robustness and a large
number of numerical experiments are presented to illustrate the gain in efficiency that
results from preconditioning. The resulting method is employed to compute approximate
solutions of the compressible Euler equations, even for very high CFL numbers.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.140214.271114a},
url = {http://global-sci.org/intro/article_detail/cicp/11014.html}
}