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ABSTRACT
Anisotropy problems are widely encountered in practical applications. In the present paper, a parallel and scalable multigrid (MG) method combined with the high-order compact difference scheme is employed to solve an anisotropy model equation on a rectangular domain. The present method is compared with the MG combined with the standard central difference scheme. Numerical results show that the MG method combined with the high-order compact difference scheme is more accurate and efficient than the MG with the standard central difference scheme for solving anisotropy elliptic problems. MG components (restriction, prolongation, relaxation, and cycling) and the corresponding parallelism characteristics are also discussed.
Nomenclature
| anb | = | coefficients of the neighbor grid points |
| ap | = | coefficient of the master grid point |
| e | = | absolute maximum errors |
| Ep | = | parallel efficiency |
| M | = | convergence rate |
| n | = | grid number |
| r | = | residual at fine grid point |
| R | = | residual at coarse grid point |
| s | = | source function |
| Sp | = | speed up |
| v | = | grid volume at fine grid point |
| V | = | grid volume at coarse grid point |
| δ | = | difference operator |
| ε | = | constant |
| Φ | = | solution variable |
| η | = | constants |
| λ | = | grid stretching parameter |
| = | Subscripts | |
| i,j,k | = | number index |
| x, y, z | = | coordinate variables |
Nomenclature
| anb | = | coefficients of the neighbor grid points |
| ap | = | coefficient of the master grid point |
| e | = | absolute maximum errors |
| Ep | = | parallel efficiency |
| M | = | convergence rate |
| n | = | grid number |
| r | = | residual at fine grid point |
| R | = | residual at coarse grid point |
| s | = | source function |
| Sp | = | speed up |
| v | = | grid volume at fine grid point |
| V | = | grid volume at coarse grid point |
| δ | = | difference operator |
| ε | = | constant |
| Φ | = | solution variable |
| η | = | constants |
| λ | = | grid stretching parameter |
| = | Subscripts | |
| i,j,k | = | number index |
| x, y, z | = | coordinate variables |