ISSN:
0029-5981
Keywords:
multigrid method
;
finite element discretization
;
matrix consistency
;
grid generation
;
Engineering
;
Numerical Methods and Modeling
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
Increasing the efficiency of solving linear/linearized matrix equations is a key point to save computer time in numerical simulation, especially for three-dimensional problems. The multigrid method has been determined to be efficient in solving boundary-value problems. However, this method is mostly linked to the finite difference discretization, rather than to the finite element discretization. This is because the grid relationship between fine and coarse grids was not achieved effectively for the latter case. Consequently, not only is the coding complicated but also the performance is not satisfactory when incorporating the multigrid method into the finite element discretization. Here we present an approach to systematically prepare necessary information to relate fine and coarse grids regarding the three-dimensional finite element discretization, such that we can take advantage of using the multigrid method. To achieve a consistent approximation at each grid, we use A2h=I2hhAhIh2h and b2h=I2hh bh, starting from the composed matrix equation of the finest grid, to prepare the matrix equations for coarse grids. Such a process is implemented on an element level to reduce the computation to its minimum. To demonstrate the performance, this approach has been used to adapt two existing three-dimensional finite element subsurface flow and transport models, 3DFEMWATER and 3DLEWASTE, to their multigrid version, 3DMGWATER and 3DMGWASTE, respectively. Two example problems, one for each model, are considered for illustration. The computational result shows that the multigrid method can help solve the example problems very efficiently with our presented modular setting. © 1998 John Wiley & Sons, Ltd.
Additional Material:
11 Ill.
Type of Medium:
Electronic Resource
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