Deflated preconditioned conjugate gradient solvers for the Pressure–Poisson equation

• Published in: Journal of computational physics Vol. 227; no. 24; pp. 10196 - 10208
• Main Authors: Aubry, Romain, Mut, Fernando, Löhner, Rainald, Cebral, Juan R.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 20-12-2008; Elsevier
• Subjects: CFD; Computational techniques; Conjugate gradients; Exact sciences and technology; Finite elements; Incompressible flow solvers; Mathematical methods in physics; Physics; Pressure–Poisson equation; CFD; Conjugate gradients; Finite elements; Incompressible flow solvers; Pressure–Poisson equation; Incompressible flow; Pressure-Poisson equation; Poisson equation; Calculation; Calculation methods
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2008.08.025

A deflated preconditioned conjugate gradient technique has been developed for the solution of the Pressure–Poisson equation within an incompressible flow solver. The deflation is done using a region-based decomposition of the unknowns, making it extremely simple to implement. The procedure has shown a considerable reduction in the number of iterations. For grids with large graph-depth the savings exceed an order of magnitude. Furthermore, the technique has shown a remarkable insensitivity to the number of groups/regions chosen, and to the way the groups are formed.