A two-level multigrid algorithm for solving a quadratic finite element models containing tetrahedral meshes is presented. The basic idea is to generate two nested finite element models, first a linear model and then a quadratic one embedded hierarchically into the linear one. The exact solution to the linear model is computed and a two-level iterative procedure is used to solve for the quadratic model. In particular, the Successive Over Relaxation (SOR) method is used for the smoothing iteration on the quadratic model in each two-level cycle. A numerical study is carried out to determine how the relaxation factor and the number of SOR iteration in each two-level cycle influence the convergence rate of the complete algorithm. The stopping criterion for the iteration is based on the notion that the error in the iterative procedure will be of the same order as the error in the finite element approximation. Finally, the efficiency of the algorithm is evaluated by comparing the computational time with that of an exact solver based on Gauss elimination. Results indicate that the present algorithm produces substantial saving of CPU time.

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