LOCAL ALGEBRAIC MULTIGRID TECHNIQUE TO ACCELERATE THE CONVERGENCE OF NUMERICAL COMPUTATION
Keywords:
Algebraic Multigrid, Acceleration Technique, Adaptive Domain, AMG, Local Algebraic MultigridAbstract
The delayed convergence of numerical computation on large sparse system of equations is caused by the low-frequency modes error and the numerical methods that deal with entire nodes on domain. This paper proposes a new method of local algebraic multigrid (LAMG) which is developed based on algebraic multigrid (AMG) and adaptive region techniques. The AMG technique used to eliminate the low-frequency modes error while the adaptive region technique used to optimize the computational regions. The defection which is combined with residual and percentage of the error was used to define the adaptive computation regions. The computational efficiency of the proposed LAMG method was evaluated by investigating on four cases of linear and nonlinear one-dimensional boundary layer equations. The predicted results are then compared with global algebraic multigrid (GAMG) method, the classical AMG, with non-adaptive region treatment. It is found that both methods, proposed LAMG and GAMG, are converged with the same number of computational cycles and same order of accuracy. The proposed LAMG, however, was executed on fewer nodes than GAMG about 13-50% and 6-14% for 1D and 2D problems, respectively, that can decrease in computational time for all the test cases.
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