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

Authors:
P. Thum;T. Clees;G. Weyns;G. Nelissen;J. Deconinck
Affiliations:
Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), Schloss Birlinghoven, D-53754 Sankt Augustin, Germany;Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), Schloss Birlinghoven, D-53754 Sankt Augustin, Germany;Vrije Universiteit Brussel, Faculty of Engineering, Department of Electrotechnical Engineering, Building Z, Pleinlaan 2, B-1050 Brussels, Belgium;Vrije Universiteit Brussel, Faculty of Engineering, Department of Electrotechnical Engineering, Building Z, Pleinlaan 2, B-1050 Brussels, Belgium;Vrije Universiteit Brussel, Faculty of Engineering, Department of Electrotechnical Engineering, Building Z, Pleinlaan 2, B-1050 Brussels, Belgium
Venue:
Journal of Computational Physics
Year:
2010

Citing 7
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The stationary semiconductor device equations

The stationary semiconductor device equations
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Semiconductor equations
A multigrid preconditioner for the semiconductor equations

SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Multigrid

Multigrid
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems
Solving unsymmetric sparse systems of linear equations with PARDISO

Future Generation Computer Systems - Special issue: Selected numerical algorithms
Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling

Journal of Computational Physics

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Abstract

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 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.