摘要
并行计算可降低时间复杂度,提高复杂计算问题的效率,有限元法存在高度的内在并行性,非常适合并行化方法的计算。因此介绍了适合并行计算的非重叠区域分解法、数据分配和数据通信的实现以及线性方程组的并行求解等。通过对二维问题进行有限元并行计算验证了该计算方法的正确性。建立了高压输电线路及其周围房屋的三维有限元模型,并对该模型划分了多个子区域通过机群来实行并行求解。结果表明,通过并行计算能精确地计算输电线路附近的房屋周围各点电场并提高计算效率;高压输电线路周围房屋对外界电场有屏蔽作用。
The time complexity can be decreased and the computational efficiency of complicated problem can be im- proved greatly by parallel computation. Non-overlapping domain decomposition method, data distribution and data communication were described. The two-dimensional finite element problem was solved first, which validated the correction of the parallel program. Then, a three-dimensional model of high voltage transmission line with the house nearby was established and decomposed into 1-6 sub-domains. The linear system of equations for each sub-domain formed separately by finite element method on the distributed memory processors was solved by krylov iterative solver. In forming the local sparse coefficient matrix, each processor was assigned a set of border and internal unknowns corresponding to a set of rows in the global sparse matrix, and external unknowns on neighboring processors were needed for the computation of border unknowns. The distributed modified sparse format DMSR （distributed modified sparse row） for parallel computation was a generalization of the MSR format used to store the local sub-matrix. The data structure consisted of an integer vector index for the column indexes and a double precision vector val for the matrix elements. Message passing was a means used widely on parallel processors with distributed memory. The basic work of message passing interface （MPI） was to transmit the data from one processor to the others. Single program multiple data （SPMD） model allowed all the processors to deal with different data under the same program. After the above calculation, the results show that parallel computation can accurately calculate the electric field around the house nearby the high voltage transmission line.
出处
《高电压技术》
EI
CAS
CSCD
北大核心
2009年第8期2000-2005,共6页
High Voltage Engineering
关键词
有限元法
区域分解法
并行计算
消息传递
输电线路
电场
finite element method
domain decomposition method
parallel computation
MPI
transmission line
electric field
