@Article{CiCP-20-4,
author = {},
title = {High Order Fixed-Point Sweeping WENO Methods for Steady State of Hyperbolic Conservation Laws and Its Convergence Study},
journal = {Communications in Computational Physics},
year = {2016},
volume = {20},
number = {4},
pages = {835--869},
abstract = {<p style="text-align: justify;">Fixed-point iterative sweeping methods were developed in the literature to
efficiently solve static Hamilton-Jacobi equations. This class of methods utilizes the
Gauss-Seidel iterations and alternating sweeping strategy to achieve fast convergence
rate. They take advantage of the properties of hyperbolic partial differential equations
(PDEs) and try to cover a family of characteristics of the corresponding Hamilton-Jacobi
equation in a certain direction simultaneously in each sweeping order. Different
from other fast sweeping methods, fixed-point iterative sweeping methods have the
advantages such as that they have explicit forms and do not involve inverse operation
of nonlinear local systems. In principle, it can be applied to solving very general
equations using any monotone numerical fluxes and high order approximations easily.
In this paper, based on the recently developed fifth order WENO schemes which improve
the convergence of the classical WENO schemes by removing slight post-shock
oscillations, we design fifth order fixed-point sweeping WENO methods for efficient
computation of steady state solution of hyperbolic conservation laws. Especially, we
show that although the methods do not have linear computational complexity, they
converge to steady state solutions much faster than regular time-marching approach
by stability improvement for high order schemes with a forward Euler time-marching.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.130715.010216a},
url = {https://global-sci.com/article/80220/high-order-fixed-point-sweeping-weno-methods-for-steady-state-of-hyperbolic-conservation-laws-and-its-convergence-study}
}