| Abstract: | We deal with the numerical solution of large linear systems resulting from discretizations of three‐dimensional boundary value problems. It has been shown recently that, if the use of presently available planewise pre‐conditionings is as pathological as thought by many people, except for some trivial anisotropic problems, linewise preconditionings could fairly outperform pointwise methods of approximately the same computational complexity. We propose here a zebra (or line red–black) like numbering strategy of the grid points that leads to a rate of convergence comparable to the one predicted for ideal planewise preconditionings. The keys to the success of this strategy are threefold. On the one hand, one gets rid of the, time and memory consuming, task of computing some accurate approximation to the inverse of each pivot plane matrix. On the other hand, at each PCG iteration, there is no longer a need to solve linear systems whose matrices have the same structure as a two‐dimensional boundary value problem matrix. Finally, it is well suited to parallel computations. Copyright © 1999 John Wiley & Sons, Ltd. |
