SHANG Yue-qiang, HE Yin-nian. A Parallel Finite Element Algorithm Based on Full Domain Partition for the Stationary Stokes Equations[J]. Applied Mathematics and Mechanics, 2010, 31(5): 609-617. doi: 10.3879/j.issn.1000-0887.2010.05.012
 Citation: SHANG Yue-qiang, HE Yin-nian. A Parallel Finite Element Algorithm Based on Full Domain Partition for the Stationary Stokes Equations[J]. Applied Mathematics and Mechanics, 2010, 31(5): 609-617.

# A Parallel Finite Element Algorithm Based on Full Domain Partition for the Stationary Stokes Equations

##### doi: 10.3879/j.issn.1000-0887.2010.05.012
• Received Date: 2009-12-18
• Rev Recd Date: 2010-04-15
• Publish Date: 2010-05-15
• Based on full domain partition, a parallel finite element algorithm for the stationary Stokes equations was proposed and analyzed. In this algorithm, each subproblem was defined in the entiredomain with the vast majority of the degrees of freedom associated with the particular subdomain that it was responsible for, and hence could be solved in parallel with other subproblems using an existing sequential solver withou textensive recoding, a llowing the algorithm to beimplemented easily with low communication costs. Some numerical results are given which demonstrate the high efficiency of the paralle lalgorithm.
•  [1] Mitchell W F. The full domain partition approach to distributing adaptive grids[J]. Appl Numer Math, 1998, 26(1/2):265-275. [2] Mitchell W F. Parallel adaptive multilevel methods with full domain partitions[J].Appl Numer Anal Comput Math, 2004, 1(1/2):36-48. [3] Adams R. Sobolev Spaces[M]. New York: Academic Press Inc，1975. [4] Ciarlet P G, Lions J L. Handbook of Numerical Analysis[M]. Vol Ⅱ，Finite Element Methods (Part Ⅰ). Amsterdam: Elsevier Science Publisher， 1991. [5] Girault V, Raviart P A. Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms[M].Berlin Heidelberg: Springer-Verlag， 1986. [6] Elman H C， Silvester D J, Wathen A J. Finite Elements and Fast Iterative Solvers:With Applications in Incompressible Fluid Dynamics[M].Oxford: Oxford University Press， 2005. [7] HE Yin-nian， XU Jin-cao， ZHOU Ai-hui, et al. Local and parallel finite element algorithms for the Stokes problem[J]. Numer Math, 2008, 109(3): 415-434.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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