| Abstract: | This paper considers the construction of high quality IBSSOR preconditionings for p-adaptive hierarchical high-order 3D FE systems. Instead of the commonly-adopted domain decomposition approach to the selection of a block partitioning underlying the corresponding block SSOR preconditioning, we introduce the so-called p-partitionings based on subdividing the degrees of freedom in accordance with the levels of p-refinement. A theoretical analysis of IBSSOR preconditionings is presented. The results of numerical experiments with 3D FE systems arising from the hierarchical approximations of order p, 3 ≤ p ≤ 5, of the 3D equilibrium equations for linear elastic orthotropic materials show that the IBSSOR preconditionings suggested are more efficient than the IBSSOR preconditionings based on domain decomposition partitionings. Moreover, we demonstrate that the new preconditionings are more reliable when solving extremely ill-conditioned 3D FE systems. © 1997 John Wiley & Sons, Ltd. |
