A FFT preconditioning technique for the solution of incompressible flow on GPUs

Mario A. Storti*, Rodrigo R. Paz, Lisandro D. Dalcin, Santiago D. Costarelli, Sergio R. Idelsohn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Graphic processing units have received much attention in last years. Compute-intensive algorithms operating on multidimensional arrays that have nearest neighbor dependency and/or exploit data locality can achieve massive speedups. Simulation of problems modeled by time-dependent Partial Differential Equations by using explicit time-stepping methods on structured grids is an instance of such GPU-friendly algorithms. Solvers for transient incompressible fluid flow cannot be developed in a fully explicit manner due to the incompressibility constraint. Segregated algorithms like the fractional step method require the solution of a Poisson problem for the pressure field at each time level. This stage is usually the most time-consuming one. This work discuss a solver for the pressure problem in applications using immersed boundary techniques in order to account for moving solid bodies. This solver is based on standard Conjugate Gradients iterations and depends on the availability of a fast Poisson solver on the whole domain to define a preconditioner. We provide a theoretical and numerical evidence on the advantages of our approach versus classical techniques based on fixed point iterations such as the Iterated Orthogonal Projection method.

Original languageEnglish (US)
Pages (from-to)44-57
Number of pages14
JournalComputers and Fluids
StatePublished - Mar 2013

Bibliographical note

Funding Information:
This work has received financial support from Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET, Argentina, PIP 5271/05), Universidad Nacional del Litoral (UNL, Argentina, Grant CAI + D 2009-65/334), Agencia Nacional de Promoción Científica y Tecnológica (ANPCyT, Argentina, grants PICT-1506/2006, PICT-1141/2007, PICT-0270/2008), and European Research Council (ERC) Advanced Grant, Real Time Computational Mechanics Techniques for Multi-Fluid Problems (REALTIME, Reference: ERC-2009-AdG). The authors made extensive use of Free Software as GNU/Linux OS, GCC/G++ compilers, Octave, and Open Source software as VTK among many others. In addition, many ideas from these packages have been inspiring to them.


  • Graphics processing units
  • Incompressible Navier-Stokes
  • Poisson equation

ASJC Scopus subject areas

  • General Computer Science
  • General Engineering


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