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| Fast and parallel algorithm design in the program for meso-mechanics analysis of concrete |
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| DOI：10.7511/jslx20083067 |
| KeyWord:meso-mechanics,finite element,sparse linear system,preconditioner,parallel algorithm |
| WU Jian-ping WANG Zheng-hua ZHU Xing-ming MA Huai-fa LI Xiao-mei |
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| Abstract: |
| For meso-mechanics analysis of concrete.This paper provides a new assembling process based on sparse matrix techniques and sparse vector techniques to generate the global stiff-matrix.The incomplete Cholesky factorization with double thresholds is incorporated into the conjugate gradient method to solve the sparse linear system.Then,the parallelization is considered in several aspects.First,an overall framework is provided to accommodate the problem.The tasks are scheduled by finite elements in the whole,but in solving sparse linear systems,the scheduling by unknowns is used.Efficient parallel algorithms are introduced for the kernels respectively,including the assembly process of the stiff matrix,incomplete Cholesky factorization with double threshold,multiplication of a sparse matrix with a dense vector,and the addition of two sparse vectors.Finally,experiments are done on a cluster of Intel Xeon processors connected with Ethernet network for two concrete samples. The first one contains 44117 discrete points and 53200 finite elements,and the second one contains 71013 discrete points and 78800 finite elements.For the first sample,the overall simulation requires 567 load steps,and the original program takes about 41 days for the whole simulation.With the improved algorithms provided in the paper,it is decreased to 6.26 hours,and with the parallel program,it is decreased further to 1.07 hours when 16 processors are used.For the second one,the overall simulation requires 94 steps,and the original program takes about 19.5 days.With the improved algorithms,it is decreased to 3.18 hours,and with the parallel program,it is decreased further to 28.4 minutes when 16 processors are used.The improvement of serial algorithms and the design of the parallel algorithms reduce the simulation time greatly,which is significant in the studies of mechanics characteristics of concrete materials. |
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