PRECONDITIONED KRYLOV SOLVERS FOR BEA

The performance of a number of preconditioned Krylov methods is analys ed for a large variety of boundary element formulations. Low- and high -order element, two-dimensional (2-D) and three-dimensional 3-D, regul ar, singular and hypersingular, collocation and symmetric Galerkin, si ngle- and multi-zone, thermal and elastic, continuous and discontinuou s boundary formulations with and without condensation are considered. Preconditioned Conjugate Gradient (CG) solvers in standard form and a form effectively operating on the normal equations (CGN), Generalized Minimal Residual (GMRES), Conjugate Gradient Squared (CGS) and Stabili zed Bi-conjugate Gradient (Bi-CGSTAB) Krylov solvers are employed in t his study. Both the primitive and preconditioned matrix operators are depicted graphically to illustrate the relative amenability of the alt ernative formulations to solution via Krylov methods, and to contrast and explain their computational performances. A notable difference bet ween 2-D and 3-D BEA operators is readily visualized in this manner. N umerical examples are presented and the relative conditioning of the v arious discrete BEA operators is reflected in the performance of the K rylov equation solvers. A preconditioning scheme which was found to be uncompetitive in the collocation BEA context is shown to make iterati ve solution of symmetric Galerkin BEA problems more economical than em ploying direct solution techniques. We conclude that the preconditione d Krylov techniques are competitive with or superior to direct methods in a wide range of boundary formulated problems, and that their perfo rmance can be partially correlated with certain problem characteristic s.