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A Parallel DDM Preconditioner for Solving Finite Element Discretization of Elasticity Problem in Three Dimension

Author: LiangWenTao
Tutor: ShuShi
School: Xiangtan University
Course: Computational Mathematics
Keywords: Three - dimensional linear elastic Preconditioner Non-overlapping domain decomposition method Algebraic multi - grid method Parallel computing
CLC: O241.82
Type: Master's thesis
Year: 2010
Downloads: 35
Quote: 0
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Abstract


Elasticity problem has a wide range of practical applications , finite element method for solving such problems most commonly used one of the discrete method , due to the finite element discrete system coefficient matrix condition number intensity depends on the grid scale , so the design of its corresponding the fast algorithm necessary . In this paper, three-dimensional linear elastic finite element linear discrete systems , non-overlapping domain decomposition method ( DDM ) and algebraic multigrid ( AMG ) combining the first to design a simple coarse space parallel non-overlapping DDM preconditioner , it is essential to the original preconditioner structural problems of linear algebra system into three types of subsystems to solve the problem . then , according to the characteristics of three types of subsystems , namely to design the corresponding fast algorithm in particular , by changing the method of classic AMG coarsening strategy ( C - AMG ) and enhance the construction method of the operator , the third class of subsystem design a new AMG ( abbreviated as AMG - T ) method . numerical results show that when the subsystem is large enough , the AMG - T method than the C - AMG method in terms of the number of iterations or has an advantage in terms of CPU time . thus obtained for solving the three - dimensional linear elastic linear element discrete systems new preconditioner Bamgddm in through the a reasonable parallel data structure design , the about parallel program Bamgddm module . numerical results show that based of the preconditioner Bamgddm the parallel PCG algorithm is efficient and robust , and has good the algorithm can be extended and parallel scalability .

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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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