@Article{IJNAM-18-5,
author = {Xiao, Mengying},
title = {An Efficient Nonlinear Solver for Steady MHD Based on Algebraic Splitting},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2021},
volume = {18},
number = {5},
pages = {674--689},
abstract = {<p style="text-align: justify;">We propose a new, efficient, nonlinear iteration for solving the steady incompressible
MHD equations. The method consists of a careful combination of an incremental Picard iteration,
Yosida splitting, and a grad-div stabilized finite element discretization. At each iteration, the Schur
complement remains the same, is SPD, and can be easily and effectively preconditioned with the
pressure mass matrix. Furthermore, this method decouples the block Schur complement into 2
simple Stokes Schur complement. We show that the iteration converges linearly to the discrete
MHD system solution, both analytically and numerically. Several numerical tests are given which
reveal very good convergence properties, and excellent results on a benchmark problem.</p>},
issn = {2617-8710},
doi = {https://doi.org/2021-IJNAM-19388},
url = {https://global-sci.com/article/82996/an-efficient-nonlinear-solver-for-steady-mhd-based-on-algebraic-splitting}
}