关键词: 多重网格, F环, 正定Holmholtz方程, 不定Helmholtz方程

Abstract: The procedure of multigrid method is described in detail and its properties are discussed by applying multigrid to both positive definite Helmholtz equation and indefinite Helmholtz equation. Comparisons of convergence performance are implemented between V cycle, W cycle and F cycle. It is shown that, by solving positive definite Helmholtz equation, multigrid method has high computing efficiency. However, as the value of wave-number increases in indefinite Helmholtz equation, the results obtained by multigrid method diverge. The reasons lie in both fine grid smoothing and coarse grid correction, and the improvement of Multigrid is still needed in future.

Key words: multigrid, F cycle, positive definite Helmholtz, indefinite Helmholtz