TY - JOUR
T1 - A Cell-Centered Multigrid Solver for the Finite Volume Discretization of Anisotropic Elliptic Interface Problems on Irregular Domains
AU - Pan , Kejia
AU - Wu , Xiaoxin
AU - Hu , Hongling
AU - Li , Zhilin
JO - Journal of Computational Mathematics
VL - 1
SP - 18
EP - 42
PY - 2024
DA - 2024/11
SN - 43
DO - http://doi.org/10.4208/jcm.2308-m2023-0029
UR - https://global-sci.org/intro/article_detail/jcm/23528.html
KW - Elliptic interface problem, Discontinuous coefficients, Anisotropic coefficients, Cascadic multigrid method, Richardson extrapolation.
AB - <p style="text-align: justify;">The aim of this paper is to develop a fast multigrid solver for interpolation-free finite
volume (FV) discretization of anisotropic elliptic interface problems on general bounded
domains that can be described as a union of blocks. We assume that the curved interface
falls exactly on the boundaries of blocks. The transfinite interpolation technique is applied
to generate block-wise distorted quadrilateral meshes, which can resolve the interface with
fine geometric details. By an extensive study of the harmonic average point method,
an interpolation-free nine-point FV scheme is then derived on such multi-block grids for
anisotropic elliptic interface problems with non-homogeneous jump conditions. Moreover,
for the resulting linear algebraic systems from cell-centered FV discretization, a high-order
prolongation operator based fast cascadic multigrid solver is developed and shown to be
robust with respect to both the problem size and the jump of the diffusion coefficients.
Various non-trivial examples including four interface problems and an elliptic problem in
complex domain without interface, all with tens of millions of unknowns, are provided to
show that the proposed multigrid solver is dozens of times faster than the classical algebraic
multigrid method as implemented in the code AMG1R5 by Stüben.</p>