The generalized global basis (GGB) method

In this work, we present the generalized global basis (GGB) method aimed at enhancing performance of multilevel solvers for difficult systems such as those arising from indefinite and non-symmetric matrices. The GGB method is based on the global basis (GB) method (Int J Numer Methods Eng 2000; 49:439–460, 461–478), which constructs an auxiliary coarse model from the largest eigenvalues of the iteration matrix. The GGB method projects these modes which would cause slow convergence to a coarse problem which is then used to eliminate these modes. Numerical examples show that best performance is obtained when GGB is accelerated by GMRES and used for problems with multiple right-hand sides. In addition, it is demonstrated that GGB method can enhance restarted GMRES strategies by retention of subspace information