A Cell-Centered Multigrid Solver for the Finite Volume Discretization of Anisotropic Elliptic Interface Problems on Irregular Domains
Year: 2025
Author: Kejia Pan, Xiaoxin Wu, Hongling Hu, Zhilin Li
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 1 : pp. 18–42
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2308-m2023-0029
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 1 : pp. 18–42
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Elliptic interface problem Discontinuous coefficients Anisotropic coefficients Cascadic multigrid method Richardson extrapolation.
Author Details
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An Edge-based cascadic multigrid method for $$H(\textbf{curl})$$ problems
Wang, Jinxuan
Pan, Kejia
Wu, Xiaoxin
(2024)
https://doi.org/10.1007/s11075-024-01917-6 [Citations: 0]