Considerable efforts in recent multigrid research have concentrated on algebraic multigrid schemes. A vital aspect of this work is uncovering algebraically smooth error modes in order to construct effective multigrid components. Many existing algebraic multigrid algorithms rely on assumptions regarding the nature of algebraic smoothness. For example, a common assumption is that smooth error is essentially constant along `strong connections'. Performance can degrade as smooth error for a problem differs from this assumption. Through tests on the homogeneous problem (Ax = 0) adaptive multigrid methods expose algebraically smooth error.

The method presented in this talk uses relaxation and subcycling on complementary grids as an evaluative tool in correcting multigrid cycling. Each complementary grid is constructed with the intent of dampening a subset of the basis of algebraically smooth error. The particular implementation of this framework manages smooth error in a manner analogous to spectral AMGe. Numerical results will be included.