New cascadic multigrid methods for two‐dimensional Poisson problem based on the fourth‐order compact difference scheme

Li, Ming; Li, Chenliang

doi:10.1002/mma.3831

Cited by 5 publications

(1 citation statement)

References 14 publications

(28 reference statements)

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“…Then the EXCMG method has been successfully applied to non-smooth elliptic problems [27,28], parabolic problems [29], and some other related problems [30][31][32]. Moreover, Pan [33] and Li [34,35] developed some EX-CMG methods combined with high-order compact difference schemes to solve Poisson equations. In 2017, Hu et al [36] obtained the super-optimality of the EXCMG method under the energy norm for H 2+α -regular (0 < α ≤ 1) elliptic problems.…”

Section: Introductionmentioning

confidence: 99%

An extrapolation full multigrid algorithm combined with fourth-order compact scheme for convection–diffusion equations

Zheng

Pan

2018

Adv Differ Equ

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In this paper, we propose an extrapolation full multigrid (EXFMG) algorithm to solve the large linear system arising from a fourth-order compact difference discretization of two-dimensional (2D) convection diffusion equations. A bi-quartic Lagrange interpolation for the solution on previous coarser grid is used to construct a good initial guess on the next finer grid for V-or W-cycles multigrid solver, which greatly reduces the number of relaxation sweeps. Instead of performing a fixed number of multigrid cycles as used in classical full multigrid methods, a series of grid level dependent relative residual tolerances is introduced to control the number of the multigrid cycles. Once the fourth-order accurate numerical solutions are obtained, a simple method based on the midpoint extrapolation is employed for the fourth-order difference solutions on two-level grids to construct a sixth-order accurate solution on the entire fine grid cheaply and directly. Numerical experiments are conducted to verify that the proposed method has much better efficiency compared to classical multigrid methods. The proposed EXFMG method can also be extended to solve other kinds of partial differential equations.

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Section: Introductionmentioning

confidence: 99%

An extrapolation full multigrid algorithm combined with fourth-order compact scheme for convection–diffusion equations

Zheng

Pan

2018

Adv Differ Equ

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An efficient algebraic multigrid method for second‐order elliptic equation on polygonal domains

2021

Math Methods in App Sciences

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Based on a coarsening strategy of adjacency matrix, a new algebraic prolongation operator is developed for standard V‐cycle multigrid method to accelerate the whole process. An efficient algebraic multigrid (EAMG) method is proposed for solving large‐scale linear system, which arise from finite element (FE) discretization of second‐order elliptic boundary value problem. Numerical experiments on polygonal domains are conducted to demonstrate that the EAMG computation is more efficient than standard method.

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Extrapolation multiscale multigrid method for solving 2D Poisson equation with sixth order compact scheme

Zheng

Pan

2018

J. Appl. Math. Comput.

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New cascadic multigrid methods for two‐dimensional Poisson problem based on the fourth‐order compact difference scheme

Cited by 5 publications

References 14 publications

An extrapolation full multigrid algorithm combined with fourth-order compact scheme for convection–diffusion equations

An extrapolation full multigrid algorithm combined with fourth-order compact scheme for convection–diffusion equations

An efficient algebraic multigrid method for second‐order elliptic equation on polygonal domains

Extrapolation multiscale multigrid method for solving 2D Poisson equation with sixth order compact scheme

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