GENERALIZED AGGREGATION MULTILEVEL SOLVER

The paper presents a Generalized Aggregation Multilevel (GAM) solver, which automatically constructs nearly optimal auxiliary coarse models based on the information available in the source grid only. GAM solver is a hybrid solution scheme where approximation space of each aggrega te (group of neighbouring elements) is adaptively and automatically se lected depending on the spectral characteristics of individual aggrega tes. Adaptive features include automated construction of auxiliary agg regated model by tracing 'stiff' and 'soft' elements, adaptive selecti on of intergrid transfer operators, and adaptive smoothing. An obstacl e test consisting of nine industry problems, such as ring-strut-ring s tructure, casting setup in airfoil, nozzle for turbines, turbine blade and diffuser casing as well as on poor conditioned shell problems, su ch as High Speed Civil Transport, automobile body and canoe, was desig ned to test the performance of GAM solver. Comparison to the state of the art direct and iterative (PCG with Incomplete Cholesky preconditio ner) is carried out. Numerical experiments indicate that GAM solver po ssesses an optimal rate of convergence by which the CPU time grows lin early with the problem size, and at the same time, robustness is not c ompromised, as its performance is almost insensitive to problem condit ioning. (C) 1997 John Wiley & Sons, Ltd.