  Efficient solution of 3D elasticity problems is an important part of many
industrial and scientific applications. Smoothed aggregation algebraic
multigrid using rigid body modes for the tentative prolongation operator
construction is an efficient and robust choice for the solution of linear
systems arising from the discretization of elasticity equations. The system
matrices on every level of the multigrid hierarchy have block structure, so
using block representation and block arithmetics should significantly improve
the solver efficiency. However, the tentative prolongation operator
construction may only be done using scalar representation. The paper proposes a
couple of practical approaches for enabling the use of block arithmetics with
smoothed aggregation algebraic multigrid based on the open-source AMGCL
library. It is shown on the example of two real-world model problems that the
suggested improvements may speed up the solution by 50% and reduce the memory
requirements for the preconditioner by 30%. The implementation is
straightforward and only requires a minimal amount of code.
