Algebraic Adaptive Multipreconditioning Applied to Restricted Additive Schwarz

摘要

In 2006 the Multipreconditioned Conjugate Gradient (MPCG) algorithm was introduced by Bridson and Greif (2006). It is an iterative linear solver, adapted from the Preconditioned Conjugate Gradient (PCG) algorithm (Saad, 2003), which can be used in cases where several preconditioners are available or the usual preconditioner is a sum of operators. In Bridson and Greif (2006) it was already pointed out that Domain Decomposition algorithms are ideal candidates to benefit from MPCG. This was further studied in Greif et al. (2014) which considers Additive Schwarz preconditioners in the Multipreconditioned GMRES (MPGMRES) Greif et al. (2016) setting. In 1997, Rixen had proposed in his thesis (Rixen, 1997) the Simultaneous FEU algorithm which turns out to be MPCG applied to FETI. The algorithm is more extensively studied in Gosselet et al. (2015) where its interpretation as an MPCG solver is made explicit.