## Abstract

Increasing the efficiency of solving linear/linearized matrix equations (Ax = b) is key to saving computer time in numerical simulation, especially for three-dimensional nonlinear problems. The multigrid method has been determined to be efficient in solving linear boundary value problems. To effectively incorporate the multigrid method into the element discretization, we have developed a modular setting for preparing information required in grid communication so that no extra work searching for relating nodes on different grids is necessary. For achieving consistent approximation on each grid, we use A^{2h} = I_{h}^{2h} A^{h}I_{2h}^{h} and b^{2h} = I_{h}^{2h} b^{h}, starting from the composed matrix equation of the finest grid, to prepare the matrix equations for coarse grids. Such a process, which was time consuming in execution on a global level due to the use of compressed coefficient matrices, is now implemented on an element level to reduce the computation to its minimum. Along with the modular setting, four multigrid/multigrid-related solvers have been developed and installed into the 3DMGWATER model. 3DMGWATER was designed to solve the Richard's equation that describes the subsurface flow through saturated/unsaturated media. A 3-D example of steady-state simulation is employed to demonstrate this study.

Original language | English |
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Pages | 543-549 |

Number of pages | 7 |

State | Published - 1996 |

Event | Proceedings of the 1996 11th International Conference on Computational Methods in Water Resources, CMWR'96. Part 1 (of 2) - Cancun, Mex Duration: 1 Jul 1996 → 1 Jul 1996 |

### Conference

Conference | Proceedings of the 1996 11th International Conference on Computational Methods in Water Resources, CMWR'96. Part 1 (of 2) |
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City | Cancun, Mex |

Period | 1/07/96 → 1/07/96 |