A new FV scheme and fast cell-centered multigrid solver for 3D anisotropic diffusion equations with discontinuous coefficients

Pan, Kejia; Wu, Xiaoxin; Hu, Hongling; Yu, Yunlong; Li, Zhilin

doi:10.1016/j.jcp.2021.110794

Cited by 11 publications

(2 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section, we first discuss some problems caused by the irregularity of geometries and discontinuity across the interface and construct a new multigrid prolongation operator, then propose a CEXCMG method for solving the large-scale linear system of equations arising from interpolation-free FV discretizations of anisotropic elliptic interface problems with homogeneous jump conditions. This work can be regarded as an extension of our previous work on the CEXCMG method for solving the large linear system resulting from FV discretizations on the regular hexahedral mesh of diffusion equations with interfaces that are parallel to the axis [39].…”

Section: The Cell-centered Extrapolation Cascadic Multigrid Methodsmentioning

confidence: 99%

A Cell-Centered Multigrid Solver for the Finite Volume Discretization of Anisotropic Elliptic Interface Problems on Irregular Domains

Pan,

Wu,

2023

JCM

View full text Add to dashboard Cite

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.

show abstract

Section: The Cell-centered Extrapolation Cascadic Multigrid Methodsmentioning

confidence: 99%

A Cell-Centered Multigrid Solver for the Finite Volume Discretization of Anisotropic Elliptic Interface Problems on Irregular Domains

Pan,

Wu,

2023

JCM

View full text Add to dashboard Cite

show abstract

“…In order to reduce computational time, Dai et al [7] developed an approximation method, where EXCMG has been used for finding a better initial guess in the MSMG method. Recently, Pan et al [23,24] applied a fast cell-centered EXCMG (CEXCMG) algorithm based on finite volume (FV) discretization to 2D/3D anisotropic diffusion equations with discontinuous coefficients.…”

Section: Introductionmentioning

confidence: 99%

An Efficient EXCMG-Newton Method Combined with Fourth-Order Compact Schemes for Semilinear Poisson Equations

Wu¹,

Pan²,

null³

et al. 2023

EAJAM

View full text Add to dashboard Cite

A fast solver for nonlinear systems arising from fourth-order compact finite difference schemes for two-dimensional semilinear Poisson equations is constructed. Applying the extrapolation and bi-quartic interpolation to two numerical solutions from the previous two levels of grids, we determine a suitable initial guess for the Newton iterations on the next finer grid. It is fifth-order accurate, which substantially reduces the number of Newton iterations required. Moreover, an extrapolated solution of sixth-order accuracy can be easily constructed on the whole fine grid. Numerical results suggest that the method is much more efficient than the existing multigrid methods for semilinear problems.

show abstract

A new finite volume scheme with gradient transfer method for solving diffusion problems on the distorted hexahedral meshes

Pan

Yuan

et al. 2022

Comput Geosci

View full text Add to dashboard Cite

A new FV scheme and fast cell-centered multigrid solver for 3D anisotropic diffusion equations with discontinuous coefficients

Cited by 11 publications

References 30 publications

A Cell-Centered Multigrid Solver for the Finite Volume Discretization of Anisotropic Elliptic Interface Problems on Irregular Domains

A Cell-Centered Multigrid Solver for the Finite Volume Discretization of Anisotropic Elliptic Interface Problems on Irregular Domains

An Efficient EXCMG-Newton Method Combined with Fourth-Order Compact Schemes for Semilinear Poisson Equations

A new finite volume scheme with gradient transfer method for solving diffusion problems on the distorted hexahedral meshes

Contact Info

Product

Resources

About