Preconditioning a Newton-Krylov solver for all-speed melt pool flow physics

Algebraic multigrid block preconditioning for multi-group radiation diffusion equations

“…The first term in (3.3) represents the "elimination" stage, while the second factor in (3.3) executes the "substitution" stage. Schur2 can be viewed as an extension to the matrix A of the primitive variable block Schur complement preconditioner proposed recently by Weston et al [39]. In the practical implementation, similar to Schur1, we take…”

“…Preconditioners of this type had been proposed and analyzed in the literature, including the block diagonal preconditioner [11,22,53], block lower / upper triangular preconditioner [2,6,9], product (splitting) preconditioner [31,38,52] and constraint preconditioner [3,12,20]. Block preconditioners with multigrid components had proven very successful in a variety of applications, e.g., liquid crystal directors modeling [5], multiphase flow in porous media [7], Stokes problem [10], incompressible Navier-Stokes problem [13], second-order Agmon-Douglis-Nirenberg elliptic systems [21], magnetohydrodynamics model [23], Dirichlet biharmonic problem [29], electrical activity in the heart [36], Brinkman problem [37], all-speed melt pool flow physics [39] and fully coupled flow and geomechanics [40]. Our focus in this work is on the block preconditioning based on the classical AMG method owing to its general applicability, high efficiency and easy-to-use user interface.…”