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Volume 25, Issue 3
Analysis of Local and Parallel Algorithm for Incompressible Magnetohydrodynamics Flows by Finite Element Iterative Method

Qili Tang & Yunqing Huang

DOI: 10.4208/cicp.OA-2017-0153

Commun. Comput. Phys., 25 (2019), pp. 729-751.

Published online: 2018-11

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  • Abstract

Based on two-grid discretizations, a local and parallel finite element algorithm (LPFEA) based on Newton iteration for solving the stationary incompressible magnetohydrodynamics (MHD) is considered in this paper. The basic idea of the algorithm is to compute the nonlinear system by Newton iteration on a globally coarse mesh first, then solve a series of subproblems of residual correction on the corresponding subdomains with fine grids in parallel. The optimal error estimates with respective to iterative step m and mesh sizes H and h≪H are derived. The efficiency of the method is illustrated by numerical experiments.

  • Keywords

Local and parallel algorithm, finite element, Newton iteration, stationary incompressible magnetohydrodynamics.

  • AMS Subject Headings

35Q30, 65M60, 65N30, 76D05

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-25-729, author = {Qili Tang and Yunqing Huang}, title = {Analysis of Local and Parallel Algorithm for Incompressible Magnetohydrodynamics Flows by Finite Element Iterative Method}, journal = {Communications in Computational Physics}, year = {2018}, volume = {25}, number = {3}, pages = {729--751}, abstract = {

Based on two-grid discretizations, a local and parallel finite element algorithm (LPFEA) based on Newton iteration for solving the stationary incompressible magnetohydrodynamics (MHD) is considered in this paper. The basic idea of the algorithm is to compute the nonlinear system by Newton iteration on a globally coarse mesh first, then solve a series of subproblems of residual correction on the corresponding subdomains with fine grids in parallel. The optimal error estimates with respective to iterative step m and mesh sizes H and h≪H are derived. The efficiency of the method is illustrated by numerical experiments.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0153}, url = {http://global-sci.org/intro/article_detail/cicp/12827.html} }
TY - JOUR T1 - Analysis of Local and Parallel Algorithm for Incompressible Magnetohydrodynamics Flows by Finite Element Iterative Method AU - Qili Tang & Yunqing Huang JO - Communications in Computational Physics VL - 3 SP - 729 EP - 751 PY - 2018 DA - 2018/11 SN - 25 DO - http://doi.org/10.4208/cicp.OA-2017-0153 UR - https://global-sci.org/intro/article_detail/cicp/12827.html KW - Local and parallel algorithm, finite element, Newton iteration, stationary incompressible magnetohydrodynamics. AB -

Based on two-grid discretizations, a local and parallel finite element algorithm (LPFEA) based on Newton iteration for solving the stationary incompressible magnetohydrodynamics (MHD) is considered in this paper. The basic idea of the algorithm is to compute the nonlinear system by Newton iteration on a globally coarse mesh first, then solve a series of subproblems of residual correction on the corresponding subdomains with fine grids in parallel. The optimal error estimates with respective to iterative step m and mesh sizes H and h≪H are derived. The efficiency of the method is illustrated by numerical experiments.

Qili Tang and Yunqing Huang. (2018). Analysis of Local and Parallel Algorithm for Incompressible Magnetohydrodynamics Flows by Finite Element Iterative Method. Communications in Computational Physics. 25 (3). 729-751. doi:10.4208/cicp.OA-2017-0153
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