Initial Guesses for Sequences of Linear Systems in a GPU-Accelerated Incompressible Flow Solver

TL;DR

This paper introduces efficient GPU-friendly initial guess methods for solving sequences of linear systems in incompressible flow simulations, demonstrating competitive performance with existing projection methods while reducing data movement.

Contribution

Proposes new stabilized polynomial extrapolation methods for initial guesses in GPU-accelerated linear system sequences, with implementations in libParanumal.

Findings

New methods are competitive with projection schemes.

Methods require less storage and data movement.

Implementations are freely available in libParanumal.

Abstract

We consider several methods for generating initial guesses when iteratively solving sequences of linear systems, showing that they can be implemented efficiently in GPU-accelerated PDE solvers, specifically solvers for incompressible flow. We propose new initial guess methods based on stabilized polynomial extrapolation and compare them to the projection method of Fischer [15], showing that they are generally competitive with projection schemes despite requiring only half the storage and performing considerably less data movement and communication. Our implementations of these algorithms are freely available as part of the libParanumal collection of GPU-accelerated flow solvers.