对称逐步超松驰预处理共轭梯度法（SSOR-PCG）是一种求解大型稀疏对称正定线性方程组的非常有效的迭代法。SSOR-PCG并行化的难点在于每步迭代都要求解2个三角方程组。采用一种改进的SSOR-PCG并行求解有限元方程组，并采用多色排序技术提高并行度。基于MPI模型开发了并行程序，通过测试，选择了有效的MPI通信函数。
Abstract
The method of symmetric successive over relaxation-preconditioned conjugate gradient (SSOR-PCG) is a very effective iterative method for solving large scale sparse symmetric positive-definite linear set of equations. The difficulty in the parallelization of the SSOR-PCG lies in solving two triangular equation systems in each iteration. In this research,an improved SSOR-PCG is applied to parallel solve finite element equations,and the multicolor ordering technique is used to increase the degree of parallelism. A MPI-based parallel program is coded and choice is made for efficient MPI communication routines by tests.
关键词
SSOR-PCG /
并行计算 /
多色排序 /
有限元方程组 /
MPI
Key words
SSOR-PCG /
parallel computing /
multicolor ordering /
finite element equations /
MPI (Message Passing Interface)
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基金
中央级公益性科研院所基本科研业务费项目（CKSF2011016）
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