TY - JOUR
T1 - Fast Solver for the Local Discontinuous Galerkin Discretization of the KdV Type Equations
AU - Ruihan Guo & Yan Xu
JO - Communications in Computational Physics
VL - 2
SP - 424
EP - 457
PY - 2018
DA - 2018/04
SN - 17
DO - http://doi.org/10.4208/cicp.210114.080814a
UR - https://global-sci.org/intro/article_detail/cicp/10964.html
KW - 
AB - <p style="text-align: justify;">In this paper, we will develop a fast iterative solver for the system of linear
equations arising from the local discontinuous Galerkin (LDG) spatial discretization
and additive Runge-Kutta (ARK) time marching method for the KdV type equations.
Being implicit in time, the severe time step ($∆t$=$\mathcal{O}(∆x^k)$, with the $k$-th order of the
partial differential equations (PDEs)) restriction for explicit methods will be removed.
The equations at the implicit time level are linear and we demonstrate an efficient,
practical multigrid (MG) method for solving the equations. In particular, we numerically
show the optimal or sub-optimal complexity of the MG solver and a two-level
local mode analysis is used to analyze the convergence behavior of the MG method.
Numerical results for one-dimensional, two-dimensional and three-dimensional cases
are given to illustrate the efficiency and capability of the LDG method coupled with
the multigrid method for solving the KdV type equations.</p>