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Abstract  

A new preconditioned conjugate gradient (PCG)-based domain decomposition method is given for the solution of linear equations arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed method is in the recommended preconditioner which is constructed by using cyclic matrix. The resulting preconditioned algorithms are well suited to parallel computation.

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A preconditioned conjugate gradient (PCG)-based domain decomposition method was given in [11] and [12] for the solution of linear equations arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed algorithm was that the recommended preconditioner was constructed by using symmetric-cyclic matrix. But we could give only the definitions of the entries of this cyclic matrix. Here we give a short description of this algorithm, the method of calculation of matrix entries and the results of calculation. The numerical experiments presented show, that this construction of precondition in the practice works well.

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In 1,118 Baosteel-university articles the top three frequently occuring keywords are “finite element OR finite element method (frequency 45)”, “mathematical model (frequency 31)” and “mathematical simulation (frequency 30)”. While in the 1,106 non

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