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Efficient algebraic multigrid for migration-diffusion-convection-reaction systems arising in electrochemical simulations

: Thum, P.; Clees, T.; Weyns, G.; Nelissen, G.; Deconinck, J.


Journal of computational physics 229 (2010), Nr.19, S.7260-7276
ISSN: 0021-9991
Fraunhofer SCAI ()
point-based algebraic multigrid; systems of partial differential equation; ILU-type smoothing; electrochemical simulation; MITReM

The article discusses components and performance of an algebraic multigrid (AMG) preconditioner 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 \'1cnite 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 scienti\'1cc 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.