TY - JOUR
T1 - Extrapolation Cascadic Multigrid Method for Cell-Centered FV Discretization of Diffusion Equations with Strongly Discontinuous and Anisotropic Coefficients
AU - Pan , Kejia
AU - Wu , Xiaoxin
AU - Yu , Yunlong
AU - Sheng , Zhiqiang
AU - Yuan , Guangwei
JO - Communications in Computational Physics
VL - 5
SP - 1561
EP - 1584
PY - 2022
DA - 2022/05
SN - 31
DO - http://doi.org/10.4208/cicp.OA-2021-0185
UR - https://global-sci.org/intro/article_detail/cicp/20515.html
KW - Diffusion equation, discontinuous coefficients, anisotropic coefficients, Richardson extrapolation, finite volume scheme, cell-centered multigrid method.
AB - <p style="text-align: justify;">Extrapolation cascadic multigrid (EXCMG) method with conjugate gradient
smoother is very efficient for solving the elliptic boundary value problems with linear
finite element discretization. However, it is not trivial to generalize the vertex-centred
EXCMG method to cell-centered finite volume (FV) methods for diffusion equations
with strongly discontinuous and anisotropic coefficients, since a non-nested hierarchy
of grid nodes are used in the cell-centered discretization. For cell-centered FV schemes,
the vertex values (auxiliary unknowns) need to be approximated by cell-centered ones
(primary unknowns). One of the novelties is to propose a new gradient transfer (GT)
method of interpolating vertex unknowns with cell-centered ones, which is easy to implement and applicable to general diffusion tensors. The main novelty of this paper is
to design a multigrid prolongation operator based on the GT method and splitting extrapolation method, and then propose a cell-centered EXCMG method with BiCGStab
smoother for solving the large linear system resulting from linear FV discretization
of diffusion equations with strongly discontinuous and anisotropic coefficients. Numerical experiments are presented to demonstrate the high efficiency of the proposed
method.</p>