Towards physics-oriented smoothing in algebraic multigrid for systems of partial differential equations arising in multi-ion transport and reaction models

Algebraic multigrid (AMG) methods offer an efficient solution technique for many industrial applications. However, the employment of AMG for physically involved systems of partial differential equations comprising convection, diffusion, migration (drift) and reaction terms is rather new. For such applications, point-based AMG (PAMG) methods are promising preconditioners. This paper focuses on developing a reordering framework for PAMG's smoothing, which is oriented on physical properties of systems arising in an electrochemical multi-ion transport and reaction model. Level-dependent, alternating smoothing is used. Numerical results are presented for a range of electrochemical test cases with scientific and industrial relevance demonstrating the robustness of the new framework. Overall, the results clearly indicate the usefulness and potentials of a physics-oriented smoothing framework.