Rigid body modes deflation of the Preconditioned Conjugate Gradient in the solution of discretized structural problems

In the numerical simulation of structural problems, a crucial aspect concern the solution of the linear system arising from the discretization of the governing equations. In fact, ill-conditioned system, related to an unfavorable eigenspectrum, are quite common in several engineering applications. In these cases the Preconditioned Conjugate Gradient enhanced with the deflation technique seems to be a very promising approach in particular because an effective deflation space is already at hand. In fact, it is possible to utilize rigid body motions of the system, that can be calculated easily and cheaply, and only the knowledge of the geometry of problem is required. This paper investigates the advantages of using a Rigid Body Modes Deflated Conjugate Gradient in the solution of challenging systems arising from structural problems. Two different situations are analyzed: the ill-conditioning caused by low constraining is addressed deflating the total rigid body modes, while the one concerning the heterogeneity of the problem by using the rigid body modes of separate components. Moreover, the implemented method is highly parallel and therefore suitable for High Performance Computing. Numerical results show how both approaches performed successfully in reducing the overall system solution time cost and iterations required for convergence.