Global-basis two-level method for indefinite systems. Part 2: computational issues

Algorithmic aspects and computational e$ciency of the global-basis two-level method are investigated in the context of symmetric inde"nite system of equations. The algorithm includes e$cient construction of the global-basis prolongator using Lanczos vectors, predictor}corrector smoothing procedures, and a heuristic two-level feedback loop aimed at ensuring convergence. Numerical experiments consisting of 3D Helmholtz equations and shear banding problems with strain softening demonstrate the excellent performance of the method