00000cab a22000003a 4500 UP-99796217608517590 Buklod 20231007234511.0 m |o d | ta 080911s xx d | ||r ||||| || (iLib)UPD-00051795339 DENGII eng Grosz, Lutz How to vectorize the algebraic multilevel iteration. Vol. 26, no. 2 pp. 293 - 309 We consider the algebraic multilevel iteration (AMLI) for the solution of systems of linear equations as they arise form a finite-difference discretization on a rectangular grid. Key operation is the matrix-vector product, which can efficiently be executed on vector and parallel-vector computer architectures if the nonzero entries of the matrix are concentrated in a few diagonals. In order to maintain this structure for all matrices on all levels coarsening in alternating directions is used. In some cases it is necessary to introduce additional dummy grid hyperplanes. The data movements in the restriction and prolongation are crucial, as they produce massive memory conflicts on vector architectures. By using a simple performance model the best of the possible vectorization strategies is automatically selected at runtime. Examples show that on a Fujitsu VPP300 the presented implementation of AMLI reaches about 85% of the useful performance, and scalability with respect to computing time can be achieved. Large linear systems. Multigrid method. Numerical software. Parallel processing. Preconditioned iterative solver. Vector computer. ACM transactions on mathematical software. 26, 2 (2000). FO UPD DENG-II Article