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Volume 42, Issue 1
Convergence Analysis of Some Finite Element Parallel Algorithms for the Stationary Incompressible MHD Equations

Xiaojing Dong & Yinnian He

DOI: 10.4208/jcm.2201-m2021-0140

J. Comp. Math., 42 (2024), pp. 49-70.

Published online: 2023-12

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  • Abstract

By combination of iteration methods with the partition of unity method (PUM), some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics (MHD) with different physical parameters are presented and analyzed. These algorithms are highly efficient. At first, a global solution is obtained on a coarse grid for all approaches by one of the iteration methods. By parallelized residual schemes, local corrected solutions are calculated on finer meshes with overlapping sub-domains. The subdomains can be achieved flexibly by a class of PUM. The proposed algorithm is proved to be uniformly stable and convergent. Finally, one numerical example is presented to confirm the theoretical findings.

  • Keywords

Partition of unity method, Local and parallel algorithm, Finite element method, Iteration methods, Magnetohydrodynamics.

  • AMS Subject Headings

35Q30, 65M60, 65N30, 76D05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-49, author = {Dong , Xiaojing and He , Yinnian}, title = {Convergence Analysis of Some Finite Element Parallel Algorithms for the Stationary Incompressible MHD Equations}, journal = {Journal of Computational Mathematics}, year = {2023}, volume = {42}, number = {1}, pages = {49--70}, abstract = {

By combination of iteration methods with the partition of unity method (PUM), some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics (MHD) with different physical parameters are presented and analyzed. These algorithms are highly efficient. At first, a global solution is obtained on a coarse grid for all approaches by one of the iteration methods. By parallelized residual schemes, local corrected solutions are calculated on finer meshes with overlapping sub-domains. The subdomains can be achieved flexibly by a class of PUM. The proposed algorithm is proved to be uniformly stable and convergent. Finally, one numerical example is presented to confirm the theoretical findings.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2201-m2021-0140}, url = {http://global-sci.org/intro/article_detail/jcm/22152.html} }
TY - JOUR T1 - Convergence Analysis of Some Finite Element Parallel Algorithms for the Stationary Incompressible MHD Equations AU - Dong , Xiaojing AU - He , Yinnian JO - Journal of Computational Mathematics VL - 1 SP - 49 EP - 70 PY - 2023 DA - 2023/12 SN - 42 DO - http://doi.org/10.4208/jcm.2201-m2021-0140 UR - https://global-sci.org/intro/article_detail/jcm/22152.html KW - Partition of unity method, Local and parallel algorithm, Finite element method, Iteration methods, Magnetohydrodynamics. AB -

By combination of iteration methods with the partition of unity method (PUM), some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics (MHD) with different physical parameters are presented and analyzed. These algorithms are highly efficient. At first, a global solution is obtained on a coarse grid for all approaches by one of the iteration methods. By parallelized residual schemes, local corrected solutions are calculated on finer meshes with overlapping sub-domains. The subdomains can be achieved flexibly by a class of PUM. The proposed algorithm is proved to be uniformly stable and convergent. Finally, one numerical example is presented to confirm the theoretical findings.

Dong , Xiaojing and He , Yinnian. (2023). Convergence Analysis of Some Finite Element Parallel Algorithms for the Stationary Incompressible MHD Equations. Journal of Computational Mathematics. 42 (1). 49-70. doi:10.4208/jcm.2201-m2021-0140
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