Additive Schwarz-based fully coupled implicit methods for resistive Hall magnetohydrodynamic problems

Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods

“…Recently progress has been made in developing fully-implicit formulations that attempt to robustly and accurately integrate these systems and follow the dynamical time-scales of interest [24,25,11,10,26,27,22,23,28,2 In Ref. [24], a nonlinear implicit MHD solver is proposed based on a implicit-operator-split (IOS) approach.…”

“…More recently, the same researchers have developed an "operator-based" parallel preconditioner for 3D MHD, based on directional splitting of the implicit operator and followed by a characteristic decomposition of the resulting directional PDE operators [30]. Reference [27] explores a Newton-Krylov-Schwarz parallel approach for the reduced Hall MHD model, where gains of an order of magnitude with respect to explicit approaches and good parallel scalability are reported. Finally, Refs.…”

NKS for Fully Coupled Fluid-Structure Interaction with Application

“…At each Newton step we solve a preconditioned linear system of the form J(y)M −1 (M s) = z for the Newton correction s, where M −1 is a one-level additive Schwarz preconditioner [10,12,13]. In this domain decomposition preconditioner, the formation of subdomains does not consider the fluid-structure boundary, so that a subdomain may contain fluid elements, structure elements, or both.…”

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“…Various numerical algorithms have been used in MHD simulations; examples include finite difference methods, finite volume methods, finite element methods, and Fourier-based spectral and pseudo-spectral methods [27]. In [12,13,14,15,21], two-dimensional, incompressible MHD problems are studied in terms of finite element approximations of the stream function-vorticity advection formulation. Since MHD flows often develop sharp interfaces, adaptive h-refinement techniques have been applied in MHD simulations [16,25,33].…”