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

• Ming Li
• Zhoushun Zheng
• Kejia Pan
Original Research

## Abstract

We present an extrapolation multiscale multigrid (EMMG) algorithm to solve the large linear systems arising from a sixth order compact discretization of the two dimensional Poisson equation, based on multigrid method and an extrapolation operator. With the help of Taylor expansion and interpolation theory, we develop three mid-point extrapolation formulas and combine it with the classical Richardson extrapolation strategy to design an extrapolation operator. Applying this proposed extrapolation operator for the sixth order difference solutions on the finest and finer grids, which have been computed by V-cycle multigrid method, we can construct an eighth order accurate extrapolation solution on the entire finest grid directly and efficiently. Moreover, we discuss the error of EMMG method in theoretically, and conduct some numerical experiments on square or reentrant domains, to verify that our EMMG algorithm can achieve eighth order convergence and keep less cost simultaneously.

## Keywords

Extrapolation Multiscale multigrid method Sixth order compact discretization Poisson equation

65N06 65N55

## Notes

### Acknowledgements

The authors would like to thank the editor and anonymous reviewers for their valuable comments and suggestions, which were helpful in improving the paper.

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© Korean Society for Computational and Applied Mathematics 2018

## Authors and Affiliations

• Ming Li
• 1
• 2
• Zhoushun Zheng
• 1
• Kejia Pan
• 1
1. 1.School of Mathematics and StatisticsCentral South UniversityChangshaChina
2. 2.Department of MathematicsHonghe UniversityMengziChina