WP4 – Communication-Optimal Algorithms for Iterative Methods

Iterative methods are widely used in large-scale academic and industrial numerical simulations for solving a linear system of equations or an eigenvalue problem. To address the scalability problem of existing iterative methods, WP4 focuses on two main aspects: the reformulation of Krylov-based iterative methods to allow a drastic reduction in the number of global communications with respect to classic formulations, and the design of communication-avoiding preconditioners to accelerate the convergence of iterative methods. The sparse direct methods developed in WP3 will be used as building blocks for the preconditioners developed.

We structure the work in this work package in three tasks:

  • Computational Kernels for Preconditioned Iterative Methods
  • Iterative Methods
  • Preconditioners

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