Generalized Aggregation Multilevel solver

摘要

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 aggregate (group of neighbouring elements) is adaptively and automatically selected depending on the spectral characteristics of individual aggregates. Adaptive features include automated construction of auxiliary aggregated model by tracing stiff and soft elements, adaptive selection of intergrid transfer operators, and adaptive smoothing. An obstacle test consisting of nine industry problems, such as ring-strut-ring structure, casting setup in airfoil, nozzle for turbines, turbine blade and diffuser casing as well as on poor conditioned shell problems, such as High Speed Civil Transport, automobile body and canoe, was designed to test the performance of GAM solver. Comparison to the state of the art direct and iterative (PCG with Incomplete Cholesky preconditioner) is carried out. Numerical experiments indicate that GAM solver possesses an optimal rate of convergence by which the CPU time grows linearly with the problem size, and at the same time, robustness is not compromised, as its performance is almost insensitive to problem conditioning.