English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Algebraic multigrid is often used as the preconditioner in Krylov subspace iterations to solve general sparse linear systems, and the aggregation based version is one of the most popular, for its cheap complexity to setup. In this paper, when this version used as the preconditioner, two schemes are provided to improve its implementation. The first is to remove the trivial computation in the smoothing for zero initial vectors before the restriction process. For this case, part of the computation is related to the multiplication of an operator to a zero vector, and then it can be omitted without any changes to the derived result. The second is to reconstruct the restriction process, which can reduce the computation complexity at the cost of a little more storage. The analyses and the numerical experiments for the solution of sparse linear systems from a model partial differential equation with preconditioned conjugate gradients show that the provided schemes can reduce the solution time significantly. The improvements are much more significant when more nodes are aggregated each time, and are more significant to W-cycle than to V-cycle and K-cycle. Keywords-aggregation based algebraic multigrid; sparse linear system; preconditioner; conjugate gradient method; computation complexity

Two Schemes to Improve the Implementation of the Aggregation Based Algebraic Multigrid Preconditioner