This talk will present a new method of adaptively constructing
smoothers based on Local Sensitivity Analysis (LSA). Given a linear
system, 
, LSA identifies blocks of the matrix, 
, so that a
smoother, such as block iterative Gauss-Seidel, can be constructed based
on the identified blocks. Results will be presented for constant and
variable coefficient elliptic problems, systems arising from scalar and
coupled system PDEs, as well as linear systems not arising from PDEs. The
simplicity of the method will allow it to be easily incorporated into
existing multigrid codes while providing a
powerful tool for adaptively constructing smoothers tuned to the
problem.