2017
DOI: 10.1016/j.jcp.2017.04.069
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A new extrapolation cascadic multigrid method for three dimensional elliptic boundary value problems

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Cited by 37 publications
(9 citation statements)
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“…Finally, we point out that solving the 3D nonlinear Allen–Cahn equations with fine grids needs a great amount of computational cost. We plan to use the newly developed extrapolation cascadic multigrid method to accelerate the computation of 3D Allen–Cahn equations in the near future.…”
Section: Conclusion and Discussion For Multi‐dimensional Allen–cahn mentioning
confidence: 99%
“…Finally, we point out that solving the 3D nonlinear Allen–Cahn equations with fine grids needs a great amount of computational cost. We plan to use the newly developed extrapolation cascadic multigrid method to accelerate the computation of 3D Allen–Cahn equations in the near future.…”
Section: Conclusion and Discussion For Multi‐dimensional Allen–cahn mentioning
confidence: 99%
“…Our future works will be focused on the convergence analysis of the CCD method and the generalization of the method for fractional order cases. And the CCD method for solving multi-dimensional elliptic boundary value problems [39][40][41][42] is also our future objective.…”
Section: Definition 1 ([35])mentioning
confidence: 99%
“…They used a V-cycle multigrid method to get the fourth-order accurate solutions on both the fine and the coarse grids first, and then chose the iterative operator with Richardson extrapolation technique to compute the sixth-order accurate solution on the fine grid. We extend the idea described in the literature [32,33,39] to the original full multigrid method, and develop an extrapolation full multigrid (EXFMG) method to solve the 2D convection-diffusion equation with a fourth-order compact difference discretization. To be more precise, a bi-quartic Lagrange interpolation operator on a coarser grid is applied to get a good initial guess on the next finer grid for the multigrid V-or W-cycles solver.…”
Section: Another Group Of Researchers Made Efforts To Design An Iteramentioning
confidence: 99%
“…This method uses a new extrapolation formula to construct a quite good initial guess for the iterative solution on the next finer grid, which greatly improves the convergence rate of the original CMG algorithm (see [24][25][26] for details). 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.…”
Section: Introductionmentioning
confidence: 99%