Convergence Stabilization of SA-AMG Method in Structural Analysis with Constraints Using Unknown Variable Transformation

Abstract

Smoothed Aggregation Algebraic Multigrid (SA-AMG) methods are known as fast methods for solving systems of simultaneous equations. When applying SA-AMG methods to systems of equations in structural analysis, it is known to converge in fewer iterations by using rigid body motion modes called near-kernel vectors. On the other hand, by transforming unknowns for equations in structural analysis, constraints such as mesh connectivity and rigid body interfaces can be imposed. In this study, it is demonstrated that by transforming near-kernel vectors in structural analysis with constraints from unknown transformations, convergence can be achieved in the same number of iterations as when no constraints are present.