Ronald Webster Stability of algebraic multigrid for Stokes problems International Journal for Numerical Methods in Fluids 71
The stability of smoothing in algebraic multigrid solvers, when applied to strongly coupled field problems (saddle-point problems), is shown to depend on the degree of coarsening in the coarse-grid approximation (CGA). Stability is most fragile for CGAs constructed with inter-grid transfer operators based on an equal-order interpolation of the scalar and vector fields. The ability of CGAs based on mixed-order interpolation to provide for a stable smoothing, and hence a mesh-independent convergence, is explained.
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