Optimized Schwarz preconditioning for SEM based magnetohydrodynamics
Incremental improvement to preconditioning for MHD simulations using spectral elements.
The authors adapted an existing Schwarz preconditioner for spectral element discretizations of magnetohydrodynamics into an optimized version, achieving improved convergence. No concrete numbers are provided.
A recent theoretical result on optimized Schwarz algorithms demonstrated at the algebraic level enables the modification of an existing Schwarz procedure to its optimized counterpart. In this work, it is shown how to modify a bilinear FEM based Schwarz preconditioning strategy originally presented in [Fischer, JCP 133:84 1997] to its optimized version. The latter is employed to precondition the pseudo--Laplacian operator arising from the spectral element discretization of the magnetohydrodynamic equations in Elsasser form.