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New interpolation operator algebraic multigrid method

Author: LiDanQing
Tutor: HuangTingZhu
School: University of Electronic Science and Technology
Course: Computational Mathematics
Keywords: Algebraic multigrid method ( AMG ) Interpolation operator Convergence
CLC: O241.82
Type: Master's thesis
Year: 2011
Downloads: 43
Quote: 0
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Abstract


In a number of complex physical systems , partial differential equations is very important mathematical model , how to obtain the exact numerical solution is an important topic in the numerical calculation for the majority of partial differential equations , numerical solution solving through discrete equations for large-scale sparse linear equations to solve the problem , iterative method is the only feasible way of solving such equations the early iterative method, such as Jacobi , Gauss - Seidel , SOR has been difficult in large - scale practical problems calculated to achieve the desired results . algebraic multigrid ( AMG ) method of its calculation of the amount of linear related to the number of unknowns , and \the basic algorithm is described , detailing the implementation of the classic AMG method AMG method is constituted mainly by the relaxation of smooth fine mesh and coarse grid correction on the two parts , on the coarse grid correction process lies in the rough spots selection and the construction of the interpolation operator we focus on the construction of the interpolation operator of a construction method is very simple interpolation operator , greatly reducing the grid complexity , reduced start-up time of the AMG method . , our classic interpolation operator in the right weight calculation method has been improved, the improved AMG method has faster convergence and wider applicable range of issues , especially for the angular scale transformation problem showing very good results . Finally, a numerical example shows that our proposed interpolation operator has a good effectiveness and robustness .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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