A fast and efficient two-grid method for solving d-dimensional poisson equations

作者：Moghaderi Hamid; Dehghan Mehdi^*; Hajarian Masoud

来源：Numerical Algorithms, 2016, 72(3): 483-537.

DOI：10.1007/s11075-015-0057-8

• Poisson equation
• Two-grid method
• Multigrid technique
• Finite difference method
• Local fourier analysis

The aim of this paper is to introduce a fast and efficient new two-grid method to solve the d-dimensional (d=1,2,3) Poisson elliptic equations. The finite difference equations at all interior grid points form a large sparse linear system, which needs to be solved efficiently. The solution cost of this sparse linear system usually dominates the total cost of solving the discretized partial differential equation. The finite difference equations are based on applying a finite difference scheme of two- and four-orders (compact finite difference method) for discretizing the spatial derivative. The obtained linear systems of Poisson elliptic equations have been solved by a new two-grid (NTG) method and we also note that the NTG method which is used for solving the large sparse linear systems is faster and more effective than that of the standard two-grid method. We utilize the local Fourier analysis to show that the spectral radius of the new two-grid method for 1D and 2D models is less than that of the standard two-grid method. As well as, we expand the corresponding algorithm to the new multi-grid method. The numerical examples show the efficiency of the new algorithms for solving the d-dimensional Poisson equations.

• 出版日期2016-7