Local and parallel finite element algorithm based on the partition of unity method for the incompressible MHD flow |
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| Authors: | Xiaojing Dong Yinnian He Hongbo Wei Yuhong Zhang |
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| Institution: | 1.Institute of Applied Physics and Computational Mathematics,Beijing,People’s Republic of China;2.Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education, School of Mathematics and Computational Science,Xiangtan University,Xiangtan,People’s Republic of China;3.School of Mathematics and Statistics,Xi’an Jiaotong University,Xi’an,People’s Republic of China;4.The 20th Research Institute of China Electronics Technology Group Corporation,Xi’an,People’s Republic of China |
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| Abstract: | Based on the partition of unity method (PUM), a local and parallel finite element method is designed and analyzed for solving the stationary incompressible magnetohydrodynamics (MHD). The key idea of the proposed algorithm is to first solve the nonlinear system on a coarse mesh, divide the globally fine grid correction into a series of locally linearized residual problems on some subdomains derived by a class of partition of unity, then compute the local subproblems in parallel, and obtain the globally continuous finite element solution by assembling all local solutions together by the partition of unity functions. The main feature of the new method is that the partition of unity provide a flexible and controllable framework for the domain decomposition. Finally, the efficiency of our theoretical analysis is tested by numerical experiments. |
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