Publications Details
ML Enhancements via the Calculation of Rigid Body Modes (RBMs) for Mechanics Problems Implemented within the Albany Code Base
The algebraic multigrid approach known as smoothed aggregation is very efficient at solving systems that arise from elasticity problems. In order to construct an efficient algebraic multilevel method, a multigrid solver should be provided with a small set of vectors that represent the error components that are difficult to resolve. It is well-known that for linear elasticity problems, these components correspond to the the so-called rigid body modes (RBMs). The present document summarizes some new development within the Albany code base that has enabled the application of algebraic multigrid preconditioners from the ML package of Trilinos to mechanics problems implemented within Albany via a new function that calculates the RBMs using information about the problem's underlying mesh. The performance of these preconditioners is evaluated on four problems: a 3D static elasticity problem, a 3D non-linear elasticity problem, a 3D thermo-elasticity problem, and a 3D thermo-poro-plasticity problem. The tests reveal the superiority of the ML preconditioners over ILU preconditioners from the Trilinos Ifpack package for mechanics problems in Albany.