Parallel finite element computation of incompressible magnetohydrodynamics based on three iterations  

作　　者：Qili TANG Yunqing HUANG 

机构地区：[1]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,Hunan Province,411105,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2022年第1期141-154,共14页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11971410 and12071404);the Natural Science Foundation of Hunan Province of China(No.2019JJ40279);the Excellent Youth Program of Scientific Research Project of Hunan Provincial Department of Education(Nos.18B064 and 20B564);the China Postdoctoral Science Foundation(Nos.2018T110073 and 2018M631402);the International Scientific and Technological Innovation Cooperation Base of Hunan Province for Computational Science(No.2018WK4006)。

摘　　要：Based on local algorithms,some parallel finite element(FE)iterative methods for stationary incompressible magnetohydrodynamics(MHD)are presented.These approaches are on account of two-grid skill include two major phases:find the FE solution by solving the nonlinear system on a globally coarse mesh to seize the low frequency component of the solution,and then locally solve linearized residual subproblems by one of three iterations(Stokes-type,Newton,and Oseen-type)on subdomains with fine grid in parallel to approximate the high frequency component.Optimal error estimates with regard to two mesh sizes and iterative steps of the proposed algorithms are given.Some numerical examples are implemented to verify the algorithm.

关 键 词：local and parallel algorithm finite element(FE)method ITERATION stationary incompressible magnetohydrodynamics(MHD) 

分 类 号：O241.82[理学—计算数学] O242.21[理学—数学]