A comparison of iterative multi-level finite element solvers

A comparison is made of two iterative algorithms: Preconditioned Conjugate Gradients (PCG) and Multigrid methods (MG), applying them to a series of test problems of plane elasticity. These problems are discretized by multilevel finite element meshes, that is, a coarse mesh whose elements are successively refined to obtain a fine mesh. In particular, uniform refinement was adopted in conjunction with triangular finite element discretizations, to;obtain the hierarchy of meshes needed by the multilevel algorithms, A numerical analysis is made of convergence criteria based on the energy variation of the incremental correction to the solution through the iterative process, which seems to be a more convenient choice to the usual criteria based on the norm of the residual. Performance comparisons are made using diagonal and hierarchical preconditioners, and in all the examples tested the hierarchical PCG is found to be faster than the multigrid solvers, (C) 1998 Elsevier Science Ltd. All rights reserved.