Efficient algebraic multigrid for migration-diffusion-convection-reaction systems arising in electrochemical simulations
The article discusses components and performance of an algebraic multigrid (AMG) pre-conditioner for the fully coupled multi-ion transport and reaction model (MITReM) with nonlinear boundary conditions, important for electrochemical modeling. The governing partial differential equations (PDEs) are discretized in space by a combined finite element and residual distribution method. Solution of the discrete system is obtained by means of a Newton-based nonlinear solver, and an AMG-preconditioned BICGSTAB Krylov linear solver. The presented AMG preconditioner is based on so-called point-based classical AMG. The linear solver is compared to a standard direct and several one-level iterative solvers for a range of geometries and chemical systems with scientific and industrial relevance. The results indicate that point-based AMG methods, carefully designed, are an attractive alternative to more commonly employed numerical methods for the simulation of complex electrochemical processes. (C) 2010 Elsevier Inc. All rights reserved.
electrochemical simulation mitrem point-based algebraic multigrid systems of partial differential equations ilu-type smoothing