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1) The algebraic multigrid method can avoid those defects.

2) The multigrid method is an efficient numerical iteration algorithm for solving elliptic variational problems.

3) Secondly,(http://sentencedict.com/multigrid.html) the W-cycle multigrid method takes less steps of iterative procedure than the V-cycle version for the same Reynolds and accuracy request.

4) The multigrid techniques are added to accelerate the convergence of flow and adjoint equations to improve the efficiency of design.

5) A computationally efficient multigrid control volume method based additive correction strategy is developed for the solution of the very high bearing number and shaped rail air bearing problems.

6) This paper proposed a cascadic multigrid(CMG) method for parabolic problems in domains with re-entrant corners, whose corresponding convergent results were obtained.

7) By use of multigrid method, this paper proposes a preconditioned iteration method solving the boundary value problem of elliptic equations, the proof of convergence is given.

8) A modified algebraic multigrid(AMG) method for queueing networks is presented.

9) An agglomeration multigrid method was applied to numerical calculation of rotor forward flight flow based upon the unstructured dynamic overset grids.

10) An efficient preconditioner is derived from the multigrid stiffness matrix.

11) We introduced volume fraction multigrid method to this parallel computing model to accelerate convergence rate of the pressure Poisson equation.

12) It is proven that the W-cycle multigrid method is optimal, i. e. , the convergence rate is independent of the mesh size and mesh level.

13) A new extrapolation cascadic multigrid method (EXCMG) is proposed based on the better initial values on refined grid provided by the new extrapolation formulas and their quadratic interpolation.

14) The pressure equation was solved by using multigrid method to achieve high computational efficiency.

15) The conjugate gradient method was applied in the prior smoothing process of the multigrid iteration procedure to improve the convergence rate.

16) In this paper, we present a new interpolation formula of algebraic multigrid (AM G ).

17) By using different mesh densities to eliminate different frequency components of errors, the multigrid method can accelerate the convergence of iteration.

18) Then a similar intergrid transfer operator is given for the spaces of velocity, and the W-cycle multigrid method is presented for solving the algebraic equations.

19) The turbulence eddy viscosity was simulated by B L model and region time steps with the multigrid techniques being used in the code in order to accelerate the convergence.

20) Computational unstructured grid is generated by advancing front method, and the structured background gird is obtained by using multigrid technique to solve the Poisson equation.

21) The capability of the solver is greatly enhanced through the use of the Multiblock and Algebraic Multigrid techniques to solve realistic problems with complex physics over complex geometries.

22) Also, the efficiency of V cycle and W cycle are compared. These results validate the possibility of the multigrid method in engineering applications.