TY - JOUR
T1 - An Efficient Nonlinear Solver for Steady MHD Based on Algebraic Splitting
AU - Xiao , Mengying
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 674
EP - 689
PY - 2021
DA - 2021/08
SN - 18
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/19388.html
KW - Steady MHD, algebraic splitting, incremental Picard Yosida method, nonlinear solver.
AB - <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>