Partial Reuse AMG Setup Cost Amortization Strategy for the Solution of Non-Steady State Problems

TL;DR

This paper introduces a partial reuse AMG setup cost amortization strategy for non-steady state problems, reducing setup costs and total compute time by reusing transfer operators across time steps.

Contribution

The paper proposes a novel partial reuse strategy for AMG setup costs specifically tailored for non-steady state problems, improving computational efficiency.

Findings

AMG setup cost reduced by 40% to 200%.

Total compute time decreased by up to 20%.

Effectiveness depends on initial setup time fraction.

Abstract

The partial reuse algebraic multigrid (AMG) setup cost amortization strategy is presented for the solution of non-steady state problems. The transfer operators are reused from the previous time steps, and the system matrices and the smoother operators are rebuilt on each of the AMG hierarchy levels. It is shown on the example of modelling a two-fluid dam break scenario that the strategy may decrease the AMG preconditioner setup cost by 40% to 200%. The total compute time is decreased by up to 20%, but the specific outcome depends on the fraction of time that the setup step initially takes.