Comparison of Second- and Fourth-Order Discretizations for Multigrid Poisson Solvers

✍ Scribed by Murli M. Gupta; Jules Kouatchou; Jun Zhang

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 247 KB
• Volume: 132
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.5466

✦ Synopsis

The multigrid method is among the most efficient iterative methods to solve linear systems arising from discretiz-

We combine a compact high-order difference approximation with multigrid V-cycle algorithm to solve the two-dimensional Poisson ing elliptic differential equations. It solves the error correcequation with Dirichlet boundary conditions. This scheme, along tion (coarse-grid-correction) sub-problem on the coarse with several different orderings of grid space and projection operagrids and interpolates the error correction solution back tors, is compared with the five-point formula to show the dramatic to the fine grids. Considerable computational time is saved improvement in computed accuracy, on serial and vector by doing major computational work on the coarse grids.

machines. ᮊ 1997 Academic Press

One iteration of a simple multigrid V-cycle consists of smoothing the error using a relaxation technique (e.g., Gauss-Seidel, Jacobi), solving an approximation to the 226